E. Nuclear and quantum physics

The diagram shows atomic transitions E₁, E₂ and E₃ when a particular atom changes its energy state. The wavelengths of the photons that correspond to these transitions are ${\lambda }_1$, ${\lambda }_2$ and ${\lambda }_3$.

What is correct for these wavelengths?

A.  ${\lambda }_1>{\lambda }_2>{\lambda }_3$

B.  ${\lambda }_1={\lambda }_2+{\lambda }_3$

C.  $\frac{1}{{\lambda }_1}=\frac{1}{{\lambda }_2+{\lambda }_3}$

D.  $\frac{1}{{\lambda }_1}=\frac{1}{{\lambda }_2}+\frac{1}{{\lambda }_3}$

Which of the following atomic energy level transitions corresponds to photons of the shortest wavelength?

The diagram shows the emission spectrum of an atom.

Which of the following atomic energy level models can produce this spectrum?

Experiments with many nuclides suggest that the radius of a nucleus is proportional to $A^{\frac{1}{3}}$, where $A$ is the number of nucleons in the nucleus. Show that the density of a nucleus remains approximately the same for all nuclei.

Four of the energy states for an atom are shown. Transition between any two states is possible.

What is the shortest wavelength of radiation that can be emitted from these four states?

A.  $\frac{hc}{E_4-E_1}$

B.  $\frac{hc}{E_4}-\frac{hc}{E_1}$

C.  $\frac{hc}{E_4-E_3}$

D.  $\frac{hc}{E_4}-\frac{hc}{E_3}$ 

The diameter of a nucleus of a particular nuclide X is $12 \mathrm{fm}$. What is the nucleon number of X?

A.  $5$

B.  $10$

C.  $125$

D.  $155$

Element X has a nucleon number $A_{\text{X}}$ and a nuclear density ${\rho }_{\text{X}}$. Element Y has a nucleon number of $2A_{\text{X}}$. What is an estimate of the nuclear density of element Y?

A.  $\frac{1}{2}{\rho }_{\text{X}}$

B.  ${\rho }_{\text{X}}$

C.  $2{\rho }_{\text{X}}$

D.  $8{\rho }_{\text{X}}$

The diagram below shows four energy levels for the atoms of a gas. The diagram is drawn to scale. The wavelengths of the photons emitted by the energy transitions between levels are shown.

What are the wavelengths of spectral lines, emitted by the gas, in order of decreasing frequency?

A.  ${\lambda }_3, {\lambda }_2, {\lambda }_1, {\lambda }_4$

B.  ${\lambda }_4, {\lambda }_1, {\lambda }_2, {\lambda }_3$

C.  ${\lambda }_4, {\lambda }_3, {\lambda }_2, {\lambda }_1$

D.  ${\lambda }_4, {\lambda }_2, {\lambda }_1, {\lambda }_3$

A student quotes three equations related to atomic and nuclear physics:

I.    $E=\frac{-13.6}{n^2}\text{eV}$

II.   $N=N_0{\text{e}}^{-\lambda t}$

III.  $mvr=\frac{nh}{2\mathrm{\pi }}$

Which equations refer to the Bohr model for hydrogen?

A.  I and II only

B.  I and III only

C.  II and III only

D.  I, II and III

The nucleus of the isotope hydrogen-2 has a radius R and a density $\rho$.

What are the approximate radius and density of a nucleus of oxygen-16?

The energy of the nth level of hydrogen is given by $-\frac{E_0}{n^2}$. What is the frequency of the photon emitted in the transition from $n=4$ to $n=2$?

A.  $\frac{1}{16}\times \frac{E_0}{h}$

B.  $\frac{3}{16}\times \frac{E_0}{h}$

C.  $\frac{1}{4}\times \frac{E_0}{h}$

D.  $\frac{3}{4}\times \frac{E_0}{h}$

An alpha particle (${}_2{}^4\text{He}$) of initial energy 5.5 MeV moves towards the centre of a nucleus of gold‑197 (${}_{79}{}^{197}\text{Au}$).

What is the distance of closest approach of the alpha particle?

A.  1.0 × 10⁻¹³ m

B.  4.1 × 10⁻¹⁴ m

C.  2.1 × 10⁻¹⁴ m

D.  6.6 × 10⁻³³ m

In an experiment, alpha particles of initial kinetic energy 5.9 MeV are directed at stationary nuclei of lead (${}_{82}{}^{207}\mathrm{Pb}$). Show that the distance of closest approach is about 4 × 10⁻¹⁴ m.

The radius of a nucleus of ${}_{82}{}^{207}\mathrm{Pb}$ is 7.1 × 10⁻¹⁵m. Explain why there will be no deviations from Rutherford scattering in the experiment in (b)(i).

In the Bohr model for hydrogen, the radius of the electron orbit in the n = 2 state is four times that of the radius in the n = 1 state.

What is $\frac{\mathrm{speed} \mathrm{of} \mathrm{the} \mathrm{electron} \mathrm{in} \mathrm{the} \mathrm{n} = 2 \mathrm{state}}{\mathrm{speed} \mathrm{of} \mathrm{the} \mathrm{electron} \mathrm{in} \mathrm{the} \mathrm{n} =1 \mathrm{state}}$?

A.  $\frac{1}{4}$

B.  $\frac{1}{2}$

C.  2

D.  4

Some energy levels for a hydrogen atom are shown.

diagram not to scale

What is the $\frac{\mathrm{wavelength} \mathrm{emitted} \mathrm{in} \mathrm{transition} \mathrm{X}}{\mathrm{wavelength} \mathrm{emitted} \mathrm{in} \mathrm{transition} \mathrm{Y}}$?

A.  $\frac{1}{2}$

B.  $\frac{27}{32}$

C.  $\frac{32}{27}$

D.  2

The energy of the nth level of hydrogen is given by $-\frac{E_0}{n^2}$. What is the frequency of the photon emitted in the transition from $n=4$ to $n=2$?

A.  $\frac{1}{16}\times \frac{E_0}{h}$

B.  $\frac{3}{16}\times \frac{E_0}{h}$

C.  $\frac{1}{4}\times \frac{E_0}{h}$

D.  $\frac{3}{4}\times \frac{E_0}{h}$

An alpha particle (${}_2{}^4\text{He}$) of initial energy 5.5 MeV moves towards the centre of a nucleus of gold‑197 (${}_{79}{}^{197}\text{Au}$).

What is the distance of closest approach of the alpha particle?

A.  1.0 × 10⁻¹³ m

B.  4.1 × 10⁻¹⁴ m

C.  2.1 × 10⁻¹⁴ m

D.  6.6 × 10⁻³³ m

The diagram shows atomic transitions E₁, E₂ and E₃ when a particular atom changes its energy state. The wavelengths of the photons that correspond to these transitions are ${\lambda }_1$, ${\lambda }_2$ and ${\lambda }_3$.

What is correct for these wavelengths?

A.  ${\lambda }_1>{\lambda }_2>{\lambda }_3$

B.  ${\lambda }_1={\lambda }_2+{\lambda }_3$

C.  $\frac{1}{{\lambda }_1}=\frac{1}{{\lambda }_2+{\lambda }_3}$

D.  $\frac{1}{{\lambda }_1}=\frac{1}{{\lambda }_2}+\frac{1}{{\lambda }_3}$

Which of the following atomic energy level transitions corresponds to photons of the shortest wavelength?

The diagram shows the emission spectrum of an atom.

Which of the following atomic energy level models can produce this spectrum?

Experiments with many nuclides suggest that the radius of a nucleus is proportional to $A^{\frac{1}{3}}$, where $A$ is the number of nucleons in the nucleus. Show that the density of a nucleus remains approximately the same for all nuclei.

Experiments with many nuclides suggest that the radius of a nucleus is proportional to $A^{\frac{1}{3}}$, where $A$ is the number of nucleons in the nucleus. Show that the density of a nucleus remains approximately the same for all nuclei.

Four of the energy states for an atom are shown. Transition between any two states is possible.

What is the shortest wavelength of radiation that can be emitted from these four states?

A.  $\frac{hc}{E_4-E_1}$

B.  $\frac{hc}{E_4}-\frac{hc}{E_1}$

C.  $\frac{hc}{E_4-E_3}$

D.  $\frac{hc}{E_4}-\frac{hc}{E_3}$ 

The diameter of a nucleus of a particular nuclide X is $12 \mathrm{fm}$. What is the nucleon number of X?

A.  $5$

B.  $10$

C.  $125$

D.  $155$

Element X has a nucleon number $A_{\text{X}}$ and a nuclear density ${\rho }_{\text{X}}$. Element Y has a nucleon number of $2A_{\text{X}}$. What is an estimate of the nuclear density of element Y?

A.  $\frac{1}{2}{\rho }_{\text{X}}$

B.  ${\rho }_{\text{X}}$

C.  $2{\rho }_{\text{X}}$

D.  $8{\rho }_{\text{X}}$

The diagram below shows four energy levels for the atoms of a gas. The diagram is drawn to scale. The wavelengths of the photons emitted by the energy transitions between levels are shown.

What are the wavelengths of spectral lines, emitted by the gas, in order of decreasing frequency?

A.  ${\lambda }_3, {\lambda }_2, {\lambda }_1, {\lambda }_4$

B.  ${\lambda }_4, {\lambda }_1, {\lambda }_2, {\lambda }_3$

C.  ${\lambda }_4, {\lambda }_3, {\lambda }_2, {\lambda }_1$

D.  ${\lambda }_4, {\lambda }_2, {\lambda }_1, {\lambda }_3$

A student quotes three equations related to atomic and nuclear physics:

I.    $E=\frac{-13.6}{n^2}\text{eV}$

II.   $N=N_0{\text{e}}^{-\lambda t}$

III.  $mvr=\frac{nh}{2\mathrm{\pi }}$

Which equations refer to the Bohr model for hydrogen?

A.  I and II only

B.  I and III only

C.  II and III only

D.  I, II and III

The nucleus of the isotope hydrogen-2 has a radius R and a density $\rho$.

What are the approximate radius and density of a nucleus of oxygen-16?

The energy of the nth level of hydrogen is given by $-\frac{E_0}{n^2}$. What is the frequency of the photon emitted in the transition from $n=4$ to $n=2$?

A.  $\frac{1}{16}\times \frac{E_0}{h}$

B.  $\frac{3}{16}\times \frac{E_0}{h}$

C.  $\frac{1}{4}\times \frac{E_0}{h}$

D.  $\frac{3}{4}\times \frac{E_0}{h}$

An alpha particle (${}_2{}^4\text{He}$) of initial energy 5.5 MeV moves towards the centre of a nucleus of gold‑197 (${}_{79}{}^{197}\text{Au}$).

What is the distance of closest approach of the alpha particle?

A.  1.0 × 10⁻¹³ m

B.  4.1 × 10⁻¹⁴ m

C.  2.1 × 10⁻¹⁴ m

D.  6.6 × 10⁻³³ m

In an experiment, alpha particles of initial kinetic energy 5.9 MeV are directed at stationary nuclei of lead (${}_{82}{}^{207}\mathrm{Pb}$). Show that the distance of closest approach is about 4 × 10⁻¹⁴ m.

The radius of a nucleus of ${}_{82}{}^{207}\mathrm{Pb}$ is 7.1 × 10⁻¹⁵m. Explain why there will be no deviations from Rutherford scattering in the experiment in (b)(i).

In an experiment, alpha particles of initial kinetic energy 5.9 MeV are directed at stationary nuclei of lead (${}_{82}{}^{207}\mathrm{Pb}$). Show that the distance of closest approach is about 4 × 10⁻¹⁴ m.

The radius of a nucleus of ${}_{82}{}^{207}\mathrm{Pb}$ is 7.1 × 10⁻¹⁵m. Explain why there will be no deviations from Rutherford scattering in the experiment in (b)(i).

In the Bohr model for hydrogen, the radius of the electron orbit in the n = 2 state is four times that of the radius in the n = 1 state.

What is $\frac{\mathrm{speed} \mathrm{of} \mathrm{the} \mathrm{electron} \mathrm{in} \mathrm{the} \mathrm{n} = 2 \mathrm{state}}{\mathrm{speed} \mathrm{of} \mathrm{the} \mathrm{electron} \mathrm{in} \mathrm{the} \mathrm{n} =1 \mathrm{state}}$?

A.  $\frac{1}{4}$

B.  $\frac{1}{2}$

C.  2

D.  4

Some energy levels for a hydrogen atom are shown.

diagram not to scale

What is the $\frac{\mathrm{wavelength} \mathrm{emitted} \mathrm{in} \mathrm{transition} \mathrm{X}}{\mathrm{wavelength} \mathrm{emitted} \mathrm{in} \mathrm{transition} \mathrm{Y}}$?

A.  $\frac{1}{2}$

B.  $\frac{27}{32}$

C.  $\frac{32}{27}$

D.  2

The energy of the nth level of hydrogen is given by $-\frac{E_0}{n^2}$. What is the frequency of the photon emitted in the transition from $n=4$ to $n=2$?

A.  $\frac{1}{16}\times \frac{E_0}{h}$

B.  $\frac{3}{16}\times \frac{E_0}{h}$

C.  $\frac{1}{4}\times \frac{E_0}{h}$

D.  $\frac{3}{4}\times \frac{E_0}{h}$

An alpha particle (${}_2{}^4\text{He}$) of initial energy 5.5 MeV moves towards the centre of a nucleus of gold‑197 (${}_{79}{}^{197}\text{Au}$).

What is the distance of closest approach of the alpha particle?

A.  1.0 × 10⁻¹³ m

B.  4.1 × 10⁻¹⁴ m

C.  2.1 × 10⁻¹⁴ m

D.  6.6 × 10⁻³³ m

The dashed line represents the variation with incident electromagnetic frequency $f$ of the kinetic energy E_K of the photoelectrons ejected from a metal surface. The metal surface is then replaced with one that requires less energy to remove an electron from the surface.

Which graph of the variation of E_K with $f$ will be observed?

Light with photons of energy 8.0 × 10⁻²⁰J are incident on a metal surface in a photoelectric experiment.

The work function of the metal surface is 4.8 × 10⁻²⁰J . What minimum voltage is required for the ammeter reading to fall to zero?

A.  0.2 V

B.  0.3 V

C.  0.5 V

D.  0.8 V

Photons of a certain frequency incident on a metal surface cause the emission of electrons from the surface. The intensity of the light is constant and the frequency of photons is increased. What is the effect, if any, on the number of emitted electrons and the energy of emitted electrons?

Calculate, in eV, the work function of the metal surface.

The intensity of the light incident on the surface is reduced by half without changing the wavelength. Draw, on the graph, the variation of the current $I$ with potential $V$ after this change.

Show that the wavelength of an electron in the beam is about $3\times {10}^{-15} \mathrm{m}$.

Outline why electrons with energy of approximately ${10}^7 \mathrm{eV}$ would be unsuitable for the investigation of nuclear radii.

A photon has a wavelength $\lambda$. What are the energy and momentum of the photon?

Show that the maximum velocity of the photoelectrons is $700 {\text{km\hspace{0.05em}\hspace{0.05em}s}}^{-1}$.

The photoelectrons are emitted from a sodium surface. Sodium has a work function of 2.3 eV.

Calculate the wavelength of the radiation incident on the sodium. State an appropriate unit for your answer.

Photons with energy 1.1 × 10⁻¹⁸J are incident on a third metal surface. The maximum energy of electrons emitted from the surface of the metal is 5.1 × 10⁻¹⁹J.

Calculate, in eV, the work function of the metal.

In a photoelectric effect experiment, a beam of light is incident on a metallic surface W in a vacuum.

The graph shows how the current $I$ varies with the potential difference V when three different beams X, Y, and Z are incident on W at different times.

            I.   X and Y have the same frequency.
            II.  Y and Z have different intensity.
            III. Y and Z have the same frequency.

Which statements are correct?

A. I and II only

B. I and III only

C. II and III only

D. I, II and III

An electron of non-relativistic speed $v$ interacts with an atom. All the energy of the electron is transferred to an emitted photon of frequency $f$ . An electron of speed $2v$ now interacts with the same atom and all its energy is transmitted to a second photon. What is the frequency of the second photon?

A.  $\frac{f}{4}$

B.  $\frac{f}{2}$

C.  $2f$

D.  $4f$

In a photoelectric experiment a stopping voltage $V$ required to prevent photoelectrons from flowing across the photoelectric cell is measured for light of two frequencies $f_1$ and $f_2$. The results obtained are shown.

The ratio $\frac{V_2-V_1}{f_2-f_1}$ is an estimate of

A.  $e$

B.  $h$

C.  $\frac{e}{h}$

D.  $\frac{h}{e}$

Monochromatic electromagnetic radiation ejects photoelectrons from a metal surface. The minimum frequency for which this is possible is $f$.

When radiation of frequency 2$f$ is incident on the surface, the kinetic energy of the photoelectrons is K.

What is the kinetic energy of the photoelectrons when the frequency of the radiation is 4$f$?

A.  K

B.  2K

C.  3K

D.  4K

A photon of wavelength $\lambda$ scatters off an electron at rest. The scattered photon has wavelength $\lambda \text{'}$.

What is the fraction of the incident photon energy that gets transferred to the electron?

A.  $\frac{\lambda }{\lambda \text{'}}$

B.  $\frac{\lambda \text{'}}{\lambda }$

C.  $\frac{\lambda \text{'}-\lambda }{\lambda }$

D.  $\frac{\lambda \text{'}-\lambda }{\lambda \text{'}}$

Monochromatic light of frequency $f_1$ is incident on the surface of a metal. The stopping voltage for this light is $V_1$. When the frequency of the radiation is changed to $f_2$, the stopping voltage is $V_2$.

What is the quantity $\frac{V_2-V_1}{f_2-f_1}$ equal to?

A.  $h$

B.  $\frac{h}{e}$

C.  $\frac{h}{c}$

D.  $\frac{hc}{e}$

An atom of hydrogen (${}_1{}^1\text{H}$) and an atom of helium (${}_2{}^4\text{He}$) are moving with the same kinetic energy.

The de Broglie wavelength of the hydrogen atom is ${\lambda }_{\text{H}}$ and the de Broglie wavelength of the helium atom is ${\lambda }_{\text{He}}$.

What is $\frac{{\lambda }_{\text{H}}}{{\lambda }_{\text{He}}}$?

A.  $\frac{1}{2}$

B.  $1$

C.  $2$

D.  $4$

Show that the energy of the scattered photon is about 16 keV.

Determine the wavelength of the incident photon.

Calculate the scattering angle of the photon.

A typical interatomic distance in the graphite crystal is of the order of $2\times {10}^{-10}$ m. Estimate the minimum value of U for the pattern in (a) to be formed on the screen.

Protons can also be accelerated by the same potential difference U. Compare, without calculation, the de Broglie wavelength of the protons to that of the electrons.

State the de Broglie hypothesis.

After passing through the circular hole the electrons strike a fluorescent screen.

Predict whether an apparatus such as this can demonstrate that moving electrons have wave properties.

The quantity $\frac{h}{m_{\text{e}}c}$ is known as the Compton wavelength.

Show that the Compton wavelength is about 2.4 pm.

Outline why the wavelength of the photon has changed.

Deduce the scattering angle for the photon.

Determine, in J, the kinetic energy of the electron after the interaction.

the work function of the surface, in eV.

the longest wavelength of a photon that will eject an electron from this surface.

Light of frequency $f$ is incident on a metallic surface of work function W. Photoelectrons with a maximum kinetic energy E_max are emitted. The frequency of the incident light is changed to 2$f$.

What is true about the maximum kinetic energy and the work function?

A photon of wavelength $\lambda$ scatters off an electron at rest. The scattered photon has wavelength $\lambda \text{'}$.

What is the fraction of the incident photon energy that gets transferred to the electron?

A.  $\frac{\lambda }{\lambda \text{'}}$

B.  $\frac{\lambda \text{'}}{\lambda }$

C.  $\frac{\lambda \text{'}-\lambda }{\lambda }$

D.  $\frac{\lambda \text{'}-\lambda }{\lambda \text{'}}$

Monochromatic light of frequency $f_1$ is incident on the surface of a metal. The stopping voltage for this light is $V_1$. When the frequency of the radiation is changed to $f_2$, the stopping voltage is $V_2$.

What is the quantity $\frac{V_2-V_1}{f_2-f_1}$ equal to?

A.  $h$

B.  $\frac{h}{e}$

C.  $\frac{h}{c}$

D.  $\frac{hc}{e}$

The dashed line represents the variation with incident electromagnetic frequency $f$ of the kinetic energy E_K of the photoelectrons ejected from a metal surface. The metal surface is then replaced with one that requires less energy to remove an electron from the surface.

Which graph of the variation of E_K with $f$ will be observed?

Light with photons of energy 8.0 × 10⁻²⁰J are incident on a metal surface in a photoelectric experiment.

The work function of the metal surface is 4.8 × 10⁻²⁰J . What minimum voltage is required for the ammeter reading to fall to zero?

A.  0.2 V

B.  0.3 V

C.  0.5 V

D.  0.8 V

Photons of a certain frequency incident on a metal surface cause the emission of electrons from the surface. The intensity of the light is constant and the frequency of photons is increased. What is the effect, if any, on the number of emitted electrons and the energy of emitted electrons?

Calculate, in eV, the work function of the metal surface.

The intensity of the light incident on the surface is reduced by half without changing the wavelength. Draw, on the graph, the variation of the current $I$ with potential $V$ after this change.

Calculate, in eV, the work function of the metal surface.

The intensity of the light incident on the surface is reduced by half without changing the wavelength. Draw, on the graph, the variation of the current $I$ with potential $V$ after this change.

Show that the wavelength of an electron in the beam is about $3\times {10}^{-15} \mathrm{m}$.

Outline why electrons with energy of approximately ${10}^7 \mathrm{eV}$ would be unsuitable for the investigation of nuclear radii.

Show that the wavelength of an electron in the beam is about $3\times {10}^{-15} \mathrm{m}$.

Outline why electrons with energy of approximately ${10}^7 \mathrm{eV}$ would be unsuitable for the investigation of nuclear radii.

A photon has a wavelength $\lambda$. What are the energy and momentum of the photon?

Show that the maximum velocity of the photoelectrons is $700 {\text{km\hspace{0.05em}\hspace{0.05em}s}}^{-1}$.

The photoelectrons are emitted from a sodium surface. Sodium has a work function of 2.3 eV.

Calculate the wavelength of the radiation incident on the sodium. State an appropriate unit for your answer.

Show that the maximum velocity of the photoelectrons is $700 {\text{km\hspace{0.05em}\hspace{0.05em}s}}^{-1}$.

The photoelectrons are emitted from a sodium surface. Sodium has a work function of 2.3 eV.

Calculate the wavelength of the radiation incident on the sodium. State an appropriate unit for your answer.

Photons with energy 1.1 × 10⁻¹⁸J are incident on a third metal surface. The maximum energy of electrons emitted from the surface of the metal is 5.1 × 10⁻¹⁹J.

Calculate, in eV, the work function of the metal.

Photons with energy 1.1 × 10⁻¹⁸J are incident on a third metal surface. The maximum energy of electrons emitted from the surface of the metal is 5.1 × 10⁻¹⁹J.

Calculate, in eV, the work function of the metal.

In a photoelectric effect experiment, a beam of light is incident on a metallic surface W in a vacuum.

The graph shows how the current $I$ varies with the potential difference V when three different beams X, Y, and Z are incident on W at different times.

            I.   X and Y have the same frequency.
            II.  Y and Z have different intensity.
            III. Y and Z have the same frequency.

Which statements are correct?

A. I and II only

B. I and III only

C. II and III only

D. I, II and III

An electron of non-relativistic speed $v$ interacts with an atom. All the energy of the electron is transferred to an emitted photon of frequency $f$ . An electron of speed $2v$ now interacts with the same atom and all its energy is transmitted to a second photon. What is the frequency of the second photon?

A.  $\frac{f}{4}$

B.  $\frac{f}{2}$

C.  $2f$

D.  $4f$

In a photoelectric experiment a stopping voltage $V$ required to prevent photoelectrons from flowing across the photoelectric cell is measured for light of two frequencies $f_1$ and $f_2$. The results obtained are shown.

The ratio $\frac{V_2-V_1}{f_2-f_1}$ is an estimate of

A.  $e$

B.  $h$

C.  $\frac{e}{h}$

D.  $\frac{h}{e}$

Monochromatic electromagnetic radiation ejects photoelectrons from a metal surface. The minimum frequency for which this is possible is $f$.

When radiation of frequency 2$f$ is incident on the surface, the kinetic energy of the photoelectrons is K.

What is the kinetic energy of the photoelectrons when the frequency of the radiation is 4$f$?

A.  K

B.  2K

C.  3K

D.  4K

A photon of wavelength $\lambda$ scatters off an electron at rest. The scattered photon has wavelength $\lambda \text{'}$.

What is the fraction of the incident photon energy that gets transferred to the electron?

A.  $\frac{\lambda }{\lambda \text{'}}$

B.  $\frac{\lambda \text{'}}{\lambda }$

C.  $\frac{\lambda \text{'}-\lambda }{\lambda }$

D.  $\frac{\lambda \text{'}-\lambda }{\lambda \text{'}}$

Monochromatic light of frequency $f_1$ is incident on the surface of a metal. The stopping voltage for this light is $V_1$. When the frequency of the radiation is changed to $f_2$, the stopping voltage is $V_2$.

What is the quantity $\frac{V_2-V_1}{f_2-f_1}$ equal to?

A.  $h$

B.  $\frac{h}{e}$

C.  $\frac{h}{c}$

D.  $\frac{hc}{e}$

An atom of hydrogen (${}_1{}^1\text{H}$) and an atom of helium (${}_2{}^4\text{He}$) are moving with the same kinetic energy.

The de Broglie wavelength of the hydrogen atom is ${\lambda }_{\text{H}}$ and the de Broglie wavelength of the helium atom is ${\lambda }_{\text{He}}$.

What is $\frac{{\lambda }_{\text{H}}}{{\lambda }_{\text{He}}}$?

A.  $\frac{1}{2}$

B.  $1$

C.  $2$

D.  $4$

Show that the energy of the scattered photon is about 16 keV.

Determine the wavelength of the incident photon.

Calculate the scattering angle of the photon.

Show that the energy of the scattered photon is about 16 keV.

Determine the wavelength of the incident photon.

Calculate the scattering angle of the photon.

A typical interatomic distance in the graphite crystal is of the order of $2\times {10}^{-10}$ m. Estimate the minimum value of U for the pattern in (a) to be formed on the screen.

Protons can also be accelerated by the same potential difference U. Compare, without calculation, the de Broglie wavelength of the protons to that of the electrons.

A typical interatomic distance in the graphite crystal is of the order of $2\times {10}^{-10}$ m. Estimate the minimum value of U for the pattern in (a) to be formed on the screen.

Protons can also be accelerated by the same potential difference U. Compare, without calculation, the de Broglie wavelength of the protons to that of the electrons.

State the de Broglie hypothesis.

After passing through the circular hole the electrons strike a fluorescent screen.

Predict whether an apparatus such as this can demonstrate that moving electrons have wave properties.

State the de Broglie hypothesis.

After passing through the circular hole the electrons strike a fluorescent screen.

Predict whether an apparatus such as this can demonstrate that moving electrons have wave properties.

The quantity $\frac{h}{m_{\text{e}}c}$ is known as the Compton wavelength.

Show that the Compton wavelength is about 2.4 pm.

Outline why the wavelength of the photon has changed.

Deduce the scattering angle for the photon.

Determine, in J, the kinetic energy of the electron after the interaction.

The quantity $\frac{h}{m_{\text{e}}c}$ is known as the Compton wavelength.

Show that the Compton wavelength is about 2.4 pm.

Outline why the wavelength of the photon has changed.

Deduce the scattering angle for the photon.

Determine, in J, the kinetic energy of the electron after the interaction.

the work function of the surface, in eV.

the longest wavelength of a photon that will eject an electron from this surface.

the work function of the surface, in eV.

the longest wavelength of a photon that will eject an electron from this surface.

Light of frequency $f$ is incident on a metallic surface of work function W. Photoelectrons with a maximum kinetic energy E_max are emitted. The frequency of the incident light is changed to 2$f$.

What is true about the maximum kinetic energy and the work function?

A photon of wavelength $\lambda$ scatters off an electron at rest. The scattered photon has wavelength $\lambda \text{'}$.

What is the fraction of the incident photon energy that gets transferred to the electron?

A.  $\frac{\lambda }{\lambda \text{'}}$

B.  $\frac{\lambda \text{'}}{\lambda }$

C.  $\frac{\lambda \text{'}-\lambda }{\lambda }$

D.  $\frac{\lambda \text{'}-\lambda }{\lambda \text{'}}$

Monochromatic light of frequency $f_1$ is incident on the surface of a metal. The stopping voltage for this light is $V_1$. When the frequency of the radiation is changed to $f_2$, the stopping voltage is $V_2$.

What is the quantity $\frac{V_2-V_1}{f_2-f_1}$ equal to?

A.  $h$

B.  $\frac{h}{e}$

C.  $\frac{h}{c}$

D.  $\frac{hc}{e}$

A radioactive nuclide X decays into a nuclide Y. The graph shows the variation with time of the activity A of X. X and Y have the same nucleon number.

What is true about nuclide X?

A.  alpha (α) emitter with a half-life of t

B.  alpha (α) emitter with a half-life of 2t

C.  beta-minus (β⁻) emitter with a half-life of t

D.  beta-minus (β⁻) emitter with a half-life of 2t

The carbon isotope $\frac{14}{6}$C is radioactive. It decays according to the equation

$\frac{14}{6}$C → $\frac{14}{7}$N + X + Y

What are X and Y?

${}_{92}{}^{238}\text{U}$ undergoes an alpha decay, followed by a beta-minus decay. What is the number of protons and neutrons in the resulting nuclide?

A pure sample of iodine-131 decays into xenon with a half-life of 8 days.

What is $\frac{\text{number of iodine atoms remaining}}{\text{number of xenon atoms formed}}$ after 24 days?

A.  $\frac{1}{8}$

B.  $\frac{1}{7}$

C.  $\frac{7}{8}$

D.  $\frac{8}{7}$

The decay constant, $\lambda$, of a radioactive sample can be defined as

A.  the number of disintegrations in the radioactive sample.

B.  the number of disintegrations per unit time in the radioactive sample.

C.  the probability that a nucleus decays in the radioactive sample.

D.  the probability that a nucleus decays per unit time in the radioactive sample.

Nuclide X can decay by two routes. In Route 1 alpha (α) decay is followed by beta-minus (β^–) decay. In Route 2 β^– decay is followed by α decay. P and R are the intermediate products and Q and S are the final products.

Which statement is correct?

A.  Q and S are different isotopes of the same element.

B.  The mass numbers of X and R are the same.

C.  The atomic numbers of P and R are the same.

D.  X and R are different isotopes of the same element.

Gamma ($\gamma$) radiation

A.  is deflected by a magnetic field.

B.  affects a photographic plate.

C.  originates in the electron cloud outside a nucleus.

D.  is deflected by an electric field.

Estimate, in Bq, the initial activity of the sample.

Calculate, in hours, the time at which the activity of the sample has decreased to one-third of the initial activity.

A radioactive nuclide with atomic number Z undergoes a process of beta-plus (β⁺) decay. What is the atomic number for the nuclide produced and what is another particle emitted during the decay?

The positions of stable nuclei are plotted by neutron number n and proton number p. The graph indicates a dotted line for which n = p. Which graph shows the line of stable nuclides and the shaded region where unstable nuclei emit beta minus (β^-) particles?

The half-life of a radioactive nuclide is 8.0 s. The initial activity of a pure sample of the nuclide is 10 000 Bq. What is the approximate activity of the sample after 4.0 s?

A. 2500 Bq

B. 5000 Bq

C. 7100 Bq

D. 7500 Bq

X is a radioactive nuclide that decays to a stable nuclide. The activity of X falls to $\frac{1}{16}$th of its original value in 32 s.
What is the half-life of X?

A.  2 s

B.  4 s

C.  8 s

D.  16 s

Calculate the binding energy per nucleon for uranium-238.

Calculate the ratio $\frac{\mathrm{kinetic} \mathrm{energy} \mathrm{of} \mathrm{alpha} \mathrm{particle}}{\mathrm{kinetic} \mathrm{energy} \mathrm{of} \mathrm{thorium} \mathrm{nucleus}}$.

A pure sample of a radioactive nuclide contains N₀ atoms at time t = 0. At time t, there are N atoms of the nuclide remaining in the sample. The half-life of the nuclide is $t_{\frac{1}{2}}$.

What is the decay rate of this sample proportional to?

A.  N

B.  N₀ – N

C.  t

D.  $t_{\frac{1}{2}}$

Samples of two radioactive nuclides X and Y are held in a container. The number of particles of X is half the number of particles of Y. The half-life of X is twice the half-life of Y.

What is the initial value of $\frac{\text{activity of radioisotope X}}{\text{activity of radioisotope Y}}$?

A.  $\frac{1}{4}$

B.  $\frac{1}{2}$

C.  $1$

D.  $4$

Which graph shows the variation of activity $A$ with time $t$ for a radioactive nuclide?

The mass of nuclear fuel in a nuclear reactor decreases at the rate of $8 \mathrm{mg}$ every hour. The overall reaction process has an efficiency of $50 \%$. What is the maximum power output of the reactor?

A.  $100 \mathrm{MW}$

B.  $200 \mathrm{MW}$

C.  $100 \mathrm{GW}$

D.  $200 \mathrm{GW}$

The rest mass of the helium isotope ${}_2^3\text{He}$ is m.

Which expression gives the binding energy per nucleon for ${}_2^3\text{He}$?

A. $\frac{(2m_p+m_n+m)c^2}{3}$

B. $\frac{(2m_p+m_n-m)c^2}{3}$

C. $(2m_p+m_n+m)c^2$

D. $(2m_p+m_n-m)c^2$

The graphs show the variation with time of the activity and the number of remaining nuclei for a sample of a radioactive nuclide.

What is the decay constant of the nuclide?

A.  ${\text{0.7\hspace{0.05em}s}}^{-1}$

B.  ${\text{1\hspace{0.05em}s}}^{-1}$

C.  $\frac{1}{0.7}{\text{\hspace{0.05em}s}}^{-1}$

D.  ${\text{1.5\hspace{0.05em}s}}^{-1}$

When a high-energy $\alpha$-particle collides with a beryllium-9 (${}_4{}^9\text{Be}$) nucleus, a nucleus of carbon $\left(\text{Z}=6\right)$ may be produced. What are the products of this reaction?

A sample of a pure radioactive nuclide initially contains $N_0$ atoms. The initial activity of the sample is $A_0$.

A second sample of the same nuclide initially contains $2N_0$ atoms.

What is the activity of the second sample after three half lives?

A.  $\frac{A_0}{2}$

B.  $\frac{A_0}{4}$

C.  $\frac{A_0}{6}$

D.  $\frac{A_0}{8}$

The mass of a nucleus of iron-56 (${}_{26}{}^{56}\text{Fe}$) is M.

What is the mass defect of the nucleus of iron-56?

A.  M − 26m_p − 56m_n

B.  26m_p + 30m_n − M

C.  M − 26m_p − 56m_n − 26m_e

D.  26m_p + 30m_n + 26m_e − M

Which property of a nuclide does not change as a result of beta decay?

A. Nucleon number

B. Neutron number

C. Proton number

D. Charge

Three particles are produced when the nuclide ${}_{12}{}^{23}\text{Mg}$ undergoes beta-plus (β⁺) decay. What are two of these particles?

A. ${}_{11}{}^{23}\text{Na}$ and ${}_0{}^0\text{v}_{\text{e}}$

B. ${}_{-1}{}^0\text{e}$ and ${}_0{}^0\text{v}_{\text{e}}$

C. ${}_{11}{}^{23}\text{Na}$ and ${}_0{}^0\overline{\text{v}}_{\text{e}}$

D. ${}_1{}^0\text{e}$ and ${}_0{}^0\overline{\text{v}}_{\text{e}}$

A pure sample of radioactive nuclide $\text{X}$ decays into a stable nuclide $\text{Y}$.

What is $\frac{\text{number of atoms of Y}}{\text{number of atoms of X}}$ after two half-lives?

A.  1

B.  2

C.  3

D.  4

Some of the nuclear energy levels of oxygen-14 (¹⁴O) and nitrogen-14 (¹⁴N) are shown.

A nucleus of ¹⁴O decays into a nucleus of ¹⁴N with the emission of a positron and a gamma ray. What is the maximum energy of the positron and the energy of the gamma ray?

What statement is not true about radioactive decay?

A.  The percentage of radioactive nuclei of an isotope in a sample of that isotope after 7 half-lives is smaller than 1 %.

B.  The half-life of a radioactive isotope is the time taken for half the nuclei in a sample of that isotope to decay.

C.  The whole-life of a radioactive isotope is the time taken for all the nuclei in a sample of that isotope to decay.

D.  The half-life of radioactive isotopes range between extremely short intervals to thousands of millions of years.

A nucleus of krypton (Kr) decays to a nucleus of bromine (Br) according to the equation

${}_{36}{}^{84}\text{Kr}\to {}_{35}{}^{84}\text{Br}+\text{Y}+\text{Z}$

What are Y and Z?

Calculate, in MeV, the energy released in this decay.

Calculate, in MeV, the energy released in this decay.

A sample contains 5.0 g of pure polonium-210. The decay constant of polonium-210 is 5.8 × 10⁻⁸ s⁻¹. Lead-206 is stable.

Calculate the mass of lead-206 present in the sample after one year.

The unified atomic mass unit, u, is a non-SI unit usually used by scientists to state atomic masses.

What is u?

A.  It is the mean of the masses of a proton and a neutron.

B.  It is the mean of the masses of protons and neutrons in all chemical elements.

C.  It is $\frac{1}{16}$ the mass of an ${}_8{}^{16}\text{O}$ atom.

D.  It is $\frac{1}{12}$ the mass of a ${}_6{}^{12}\text{C}$ atom.

Two radioactive samples $\mathrm{X}$ and $\mathrm{Y}$ have the same half-life. Initially the ratio $\frac{\mathrm{activity} \mathrm{of} \mathrm{X}}{\mathrm{activity} \mathrm{of} \mathrm{Y}}$ is 4.

What is this ratio after 2 half-lives?

A.  $\frac{1}{2}$

B.  1

C.  2

D.  4

Calculate the maximum current in the chamber due to the electrons when there is no smoke in the chamber.

Calculate the maximum current in the chamber due to the electrons when there is no smoke in the chamber.

State and explain the decay mode of ${}_{52}{}^{132}\text{Te}$.

Calculate, in s⁻¹, the initial activity of the sample.

Show that the decay constant of a nuclide is given by −m, where m is the slope of the graph of lnA against t.

Determine, in days, the half-life of ${}_{52}{}^{132}\text{Te}$.

Show that the energy released is about 18 MeV.

State the nucleon number of the He isotope that ${}_1{}^3\mathrm{H}$ decays into.

Estimate the fraction of tritium remaining after one year.

Show that the energy released is about 18 MeV.

State the nucleon number of the He isotope that ${}_1{}^3\mathrm{H}$ decays into.

Show, using the data, that the energy released in the decay of one magnesium-27 nucleus is about 2.62 MeV.

Mass of aluminium-27 atom = 26.98153 u
Mass of magnesium-27 atom = 26.98434 u
The unified atomic mass unit is 931.5 MeV c⁻².

Calculate the difference between the magnitudes of the total energy transfers in parts (a) and (b).

Explain how the difference in part (b)(ii) arises.

The smallest mass of magnesium that can be detected with this technique is 1.1 × 10⁻⁸ kg.

Show that the smallest number of magnesium atoms that can be detected with this technique is about 10¹⁷.

A sample of glass is irradiated with neutrons so that all the magnesium atoms become magnesium-27. The sample contains 9.50 × 10¹⁵ magnesium atoms.

The decay constant of magnesium-27 is 1.22 × 10⁻³ s⁻¹.

Determine the number of aluminium atoms that form in 10.0 minutes after the irradiation ends.

Estimate, in W, the average rate at which energy is transferred by the decay of magnesium-27 during the 10.0 minutes after the irradiation ends.

Radioactive nuclide X decays into a stable nuclide Y. The decay constant of X is λ. The variation with time t of number of nuclei of X and Y are shown on the same axes.

What is the expression for s?

A.  $\frac{\ln 2}{\lambda }$

B.  $\frac{1}{\lambda }$

C.  $\frac{\lambda }{\ln 2}$

D.  $\ln 2$

A nucleus of platinum (Pt) undergoes alpha decay to form an osmium (Os) nucleus as represented by the following reaction.

${}_{78}{}^{175}\mathrm{Pt}$ → Os + alpha particle

What are the number of protons and the number of neutrons in the osmium nucleus?

Calculate, in MeV, the energy released in the reaction.

Two nuclides present in spent nuclear fuel ${}_{55}{}^{137}\text{Cs}$ are  and cerium-144 (${}_{58}{}^{144}\text{Ce}$). The initial activity of a sample of pure ${}_{58}{}^{144}\text{Ce}$ is about 40 times greater than the activity of the same amount of pure ${}_{55}{}^{137}\text{Cs}$.

Discuss which of the two nuclides is more likely to require long-term storage once removed from the reactor.

Every neutron-induced fission reaction of uranium-235 releases an energy of about 200 MeV. A nuclear power station transfers an energy of about 2.4 GJ per second.

Determine the mass of uranium-235 that undergoes fission in one day in this power station.

Two radioactive samples $\mathrm{X}$ and $\mathrm{Y}$ have the same half-life. Initially the ratio $\frac{\mathrm{activity} \mathrm{of} \mathrm{X}}{\mathrm{activity} \mathrm{of} \mathrm{Y}}$ is 4.

What is this ratio after 2 half-lives?

A.  $\frac{1}{2}$

B.  1

C.  2

D.  4

Two radioactive samples $\mathrm{X}$ and $\mathrm{Y}$ have the same half-life. Initially the ratio $\frac{\mathrm{activity} \mathrm{of} \mathrm{X}}{\mathrm{activity} \mathrm{of} \mathrm{Y}}$ is 4.

What is this ratio after 2 half-lives?

A.  $\frac{1}{2}$

B.  1

C.  2

D.  4

Calculate the maximum current in the chamber due to the electrons when there is no smoke in the chamber.

A radioactive nuclide X decays into a nuclide Y. The graph shows the variation with time of the activity A of X. X and Y have the same nucleon number.

What is true about nuclide X?

A.  alpha (α) emitter with a half-life of t

B.  alpha (α) emitter with a half-life of 2t

C.  beta-minus (β⁻) emitter with a half-life of t

D.  beta-minus (β⁻) emitter with a half-life of 2t

The carbon isotope $\frac{14}{6}$C is radioactive. It decays according to the equation

$\frac{14}{6}$C → $\frac{14}{7}$N + X + Y

What are X and Y?

${}_{92}{}^{238}\text{U}$ undergoes an alpha decay, followed by a beta-minus decay. What is the number of protons and neutrons in the resulting nuclide?

A pure sample of iodine-131 decays into xenon with a half-life of 8 days.

What is $\frac{\text{number of iodine atoms remaining}}{\text{number of xenon atoms formed}}$ after 24 days?

A.  $\frac{1}{8}$

B.  $\frac{1}{7}$

C.  $\frac{7}{8}$

D.  $\frac{8}{7}$

The decay constant, $\lambda$, of a radioactive sample can be defined as

A.  the number of disintegrations in the radioactive sample.

B.  the number of disintegrations per unit time in the radioactive sample.

C.  the probability that a nucleus decays in the radioactive sample.

D.  the probability that a nucleus decays per unit time in the radioactive sample.

Nuclide X can decay by two routes. In Route 1 alpha (α) decay is followed by beta-minus (β^–) decay. In Route 2 β^– decay is followed by α decay. P and R are the intermediate products and Q and S are the final products.

Which statement is correct?

A.  Q and S are different isotopes of the same element.

B.  The mass numbers of X and R are the same.

C.  The atomic numbers of P and R are the same.

D.  X and R are different isotopes of the same element.

Gamma ($\gamma$) radiation

A.  is deflected by a magnetic field.

B.  affects a photographic plate.

C.  originates in the electron cloud outside a nucleus.

D.  is deflected by an electric field.

Estimate, in Bq, the initial activity of the sample.

Calculate, in hours, the time at which the activity of the sample has decreased to one-third of the initial activity.

Estimate, in Bq, the initial activity of the sample.

Calculate, in hours, the time at which the activity of the sample has decreased to one-third of the initial activity.

A radioactive nuclide with atomic number Z undergoes a process of beta-plus (β⁺) decay. What is the atomic number for the nuclide produced and what is another particle emitted during the decay?

The positions of stable nuclei are plotted by neutron number n and proton number p. The graph indicates a dotted line for which n = p. Which graph shows the line of stable nuclides and the shaded region where unstable nuclei emit beta minus (β^-) particles?

The half-life of a radioactive nuclide is 8.0 s. The initial activity of a pure sample of the nuclide is 10 000 Bq. What is the approximate activity of the sample after 4.0 s?

A. 2500 Bq

B. 5000 Bq

C. 7100 Bq

D. 7500 Bq

X is a radioactive nuclide that decays to a stable nuclide. The activity of X falls to $\frac{1}{16}$th of its original value in 32 s.
What is the half-life of X?

A.  2 s

B.  4 s

C.  8 s

D.  16 s

Calculate the binding energy per nucleon for uranium-238.

Calculate the ratio $\frac{\mathrm{kinetic} \mathrm{energy} \mathrm{of} \mathrm{alpha} \mathrm{particle}}{\mathrm{kinetic} \mathrm{energy} \mathrm{of} \mathrm{thorium} \mathrm{nucleus}}$.

Calculate the binding energy per nucleon for uranium-238.

Calculate the ratio $\frac{\mathrm{kinetic} \mathrm{energy} \mathrm{of} \mathrm{alpha} \mathrm{particle}}{\mathrm{kinetic} \mathrm{energy} \mathrm{of} \mathrm{thorium} \mathrm{nucleus}}$.

A pure sample of a radioactive nuclide contains N₀ atoms at time t = 0. At time t, there are N atoms of the nuclide remaining in the sample. The half-life of the nuclide is $t_{\frac{1}{2}}$.

What is the decay rate of this sample proportional to?

A.  N

B.  N₀ – N

C.  t

D.  $t_{\frac{1}{2}}$

Samples of two radioactive nuclides X and Y are held in a container. The number of particles of X is half the number of particles of Y. The half-life of X is twice the half-life of Y.

What is the initial value of $\frac{\text{activity of radioisotope X}}{\text{activity of radioisotope Y}}$?

A.  $\frac{1}{4}$

B.  $\frac{1}{2}$

C.  $1$

D.  $4$

Which graph shows the variation of activity $A$ with time $t$ for a radioactive nuclide?

The mass of nuclear fuel in a nuclear reactor decreases at the rate of $8 \mathrm{mg}$ every hour. The overall reaction process has an efficiency of $50 \%$. What is the maximum power output of the reactor?

A.  $100 \mathrm{MW}$

B.  $200 \mathrm{MW}$

C.  $100 \mathrm{GW}$

D.  $200 \mathrm{GW}$

The rest mass of the helium isotope ${}_2^3\text{He}$ is m.

Which expression gives the binding energy per nucleon for ${}_2^3\text{He}$?

A. $\frac{(2m_p+m_n+m)c^2}{3}$

B. $\frac{(2m_p+m_n-m)c^2}{3}$

C. $(2m_p+m_n+m)c^2$

D. $(2m_p+m_n-m)c^2$

The graphs show the variation with time of the activity and the number of remaining nuclei for a sample of a radioactive nuclide.

What is the decay constant of the nuclide?

A.  ${\text{0.7\hspace{0.05em}s}}^{-1}$

B.  ${\text{1\hspace{0.05em}s}}^{-1}$

C.  $\frac{1}{0.7}{\text{\hspace{0.05em}s}}^{-1}$

D.  ${\text{1.5\hspace{0.05em}s}}^{-1}$

When a high-energy $\alpha$-particle collides with a beryllium-9 (${}_4{}^9\text{Be}$) nucleus, a nucleus of carbon $\left(\text{Z}=6\right)$ may be produced. What are the products of this reaction?

A sample of a pure radioactive nuclide initially contains $N_0$ atoms. The initial activity of the sample is $A_0$.

A second sample of the same nuclide initially contains $2N_0$ atoms.

What is the activity of the second sample after three half lives?

A.  $\frac{A_0}{2}$

B.  $\frac{A_0}{4}$

C.  $\frac{A_0}{6}$

D.  $\frac{A_0}{8}$

The mass of a nucleus of iron-56 (${}_{26}{}^{56}\text{Fe}$) is M.

What is the mass defect of the nucleus of iron-56?

A.  M − 26m_p − 56m_n

B.  26m_p + 30m_n − M

C.  M − 26m_p − 56m_n − 26m_e

D.  26m_p + 30m_n + 26m_e − M

Which property of a nuclide does not change as a result of beta decay?

A. Nucleon number

B. Neutron number

C. Proton number

D. Charge

Three particles are produced when the nuclide ${}_{12}{}^{23}\text{Mg}$ undergoes beta-plus (β⁺) decay. What are two of these particles?

A. ${}_{11}{}^{23}\text{Na}$ and ${}_0{}^0\text{v}_{\text{e}}$

B. ${}_{-1}{}^0\text{e}$ and ${}_0{}^0\text{v}_{\text{e}}$

C. ${}_{11}{}^{23}\text{Na}$ and ${}_0{}^0\overline{\text{v}}_{\text{e}}$

D. ${}_1{}^0\text{e}$ and ${}_0{}^0\overline{\text{v}}_{\text{e}}$

A pure sample of radioactive nuclide $\text{X}$ decays into a stable nuclide $\text{Y}$.

What is $\frac{\text{number of atoms of Y}}{\text{number of atoms of X}}$ after two half-lives?

A.  1

B.  2

C.  3

D.  4

Some of the nuclear energy levels of oxygen-14 (¹⁴O) and nitrogen-14 (¹⁴N) are shown.

A nucleus of ¹⁴O decays into a nucleus of ¹⁴N with the emission of a positron and a gamma ray. What is the maximum energy of the positron and the energy of the gamma ray?

What statement is not true about radioactive decay?

A.  The percentage of radioactive nuclei of an isotope in a sample of that isotope after 7 half-lives is smaller than 1 %.

B.  The half-life of a radioactive isotope is the time taken for half the nuclei in a sample of that isotope to decay.

C.  The whole-life of a radioactive isotope is the time taken for all the nuclei in a sample of that isotope to decay.

D.  The half-life of radioactive isotopes range between extremely short intervals to thousands of millions of years.

A nucleus of krypton (Kr) decays to a nucleus of bromine (Br) according to the equation

${}_{36}{}^{84}\text{Kr}\to {}_{35}{}^{84}\text{Br}+\text{Y}+\text{Z}$

What are Y and Z?

Calculate, in MeV, the energy released in this decay.

Calculate, in MeV, the energy released in this decay.

Calculate, in MeV, the energy released in this decay.

A sample contains 5.0 g of pure polonium-210. The decay constant of polonium-210 is 5.8 × 10⁻⁸ s⁻¹. Lead-206 is stable.

Calculate the mass of lead-206 present in the sample after one year.

Calculate, in MeV, the energy released in this decay.

A sample contains 5.0 g of pure polonium-210. The decay constant of polonium-210 is 5.8 × 10⁻⁸ s⁻¹. Lead-206 is stable.

Calculate the mass of lead-206 present in the sample after one year.

The unified atomic mass unit, u, is a non-SI unit usually used by scientists to state atomic masses.

What is u?

A.  It is the mean of the masses of a proton and a neutron.

B.  It is the mean of the masses of protons and neutrons in all chemical elements.

C.  It is $\frac{1}{16}$ the mass of an ${}_8{}^{16}\text{O}$ atom.

D.  It is $\frac{1}{12}$ the mass of a ${}_6{}^{12}\text{C}$ atom.

Two radioactive samples $\mathrm{X}$ and $\mathrm{Y}$ have the same half-life. Initially the ratio $\frac{\mathrm{activity} \mathrm{of} \mathrm{X}}{\mathrm{activity} \mathrm{of} \mathrm{Y}}$ is 4.

What is this ratio after 2 half-lives?

A.  $\frac{1}{2}$

B.  1

C.  2

D.  4

Calculate the maximum current in the chamber due to the electrons when there is no smoke in the chamber.

Calculate the maximum current in the chamber due to the electrons when there is no smoke in the chamber.

Calculate the maximum current in the chamber due to the electrons when there is no smoke in the chamber.

Calculate the maximum current in the chamber due to the electrons when there is no smoke in the chamber.

State and explain the decay mode of ${}_{52}{}^{132}\text{Te}$.

Calculate, in s⁻¹, the initial activity of the sample.

Show that the decay constant of a nuclide is given by −m, where m is the slope of the graph of lnA against t.

Determine, in days, the half-life of ${}_{52}{}^{132}\text{Te}$.

State and explain the decay mode of ${}_{52}{}^{132}\text{Te}$.

Calculate, in s⁻¹, the initial activity of the sample.

Show that the decay constant of a nuclide is given by −m, where m is the slope of the graph of lnA against t.

Determine, in days, the half-life of ${}_{52}{}^{132}\text{Te}$.

Show that the energy released is about 18 MeV.

State the nucleon number of the He isotope that ${}_1{}^3\mathrm{H}$ decays into.

Estimate the fraction of tritium remaining after one year.

Show that the energy released is about 18 MeV.

State the nucleon number of the He isotope that ${}_1{}^3\mathrm{H}$ decays into.

Estimate the fraction of tritium remaining after one year.

Show that the energy released is about 18 MeV.

State the nucleon number of the He isotope that ${}_1{}^3\mathrm{H}$ decays into.

Show that the energy released is about 18 MeV.

State the nucleon number of the He isotope that ${}_1{}^3\mathrm{H}$ decays into.

Show, using the data, that the energy released in the decay of one magnesium-27 nucleus is about 2.62 MeV.

Mass of aluminium-27 atom = 26.98153 u
Mass of magnesium-27 atom = 26.98434 u
The unified atomic mass unit is 931.5 MeV c⁻².

Calculate the difference between the magnitudes of the total energy transfers in parts (a) and (b).

Explain how the difference in part (b)(ii) arises.

The smallest mass of magnesium that can be detected with this technique is 1.1 × 10⁻⁸ kg.

Show that the smallest number of magnesium atoms that can be detected with this technique is about 10¹⁷.

A sample of glass is irradiated with neutrons so that all the magnesium atoms become magnesium-27. The sample contains 9.50 × 10¹⁵ magnesium atoms.

The decay constant of magnesium-27 is 1.22 × 10⁻³ s⁻¹.

Determine the number of aluminium atoms that form in 10.0 minutes after the irradiation ends.

Estimate, in W, the average rate at which energy is transferred by the decay of magnesium-27 during the 10.0 minutes after the irradiation ends.

Show, using the data, that the energy released in the decay of one magnesium-27 nucleus is about 2.62 MeV.

Mass of aluminium-27 atom = 26.98153 u
Mass of magnesium-27 atom = 26.98434 u
The unified atomic mass unit is 931.5 MeV c⁻².

Calculate the difference between the magnitudes of the total energy transfers in parts (a) and (b).

Explain how the difference in part (b)(ii) arises.

The smallest mass of magnesium that can be detected with this technique is 1.1 × 10⁻⁸ kg.

Show that the smallest number of magnesium atoms that can be detected with this technique is about 10¹⁷.

A sample of glass is irradiated with neutrons so that all the magnesium atoms become magnesium-27. The sample contains 9.50 × 10¹⁵ magnesium atoms.

The decay constant of magnesium-27 is 1.22 × 10⁻³ s⁻¹.

Determine the number of aluminium atoms that form in 10.0 minutes after the irradiation ends.

Estimate, in W, the average rate at which energy is transferred by the decay of magnesium-27 during the 10.0 minutes after the irradiation ends.

Radioactive nuclide X decays into a stable nuclide Y. The decay constant of X is λ. The variation with time t of number of nuclei of X and Y are shown on the same axes.

What is the expression for s?

A.  $\frac{\ln 2}{\lambda }$

B.  $\frac{1}{\lambda }$

C.  $\frac{\lambda }{\ln 2}$

D.  $\ln 2$

A nucleus of platinum (Pt) undergoes alpha decay to form an osmium (Os) nucleus as represented by the following reaction.

${}_{78}{}^{175}\mathrm{Pt}$ → Os + alpha particle

What are the number of protons and the number of neutrons in the osmium nucleus?

Calculate, in MeV, the energy released in the reaction.

Two nuclides present in spent nuclear fuel ${}_{55}{}^{137}\text{Cs}$ are  and cerium-144 (${}_{58}{}^{144}\text{Ce}$). The initial activity of a sample of pure ${}_{58}{}^{144}\text{Ce}$ is about 40 times greater than the activity of the same amount of pure ${}_{55}{}^{137}\text{Cs}$.

Discuss which of the two nuclides is more likely to require long-term storage once removed from the reactor.

Calculate, in MeV, the energy released in the reaction.

Two nuclides present in spent nuclear fuel ${}_{55}{}^{137}\text{Cs}$ are  and cerium-144 (${}_{58}{}^{144}\text{Ce}$). The initial activity of a sample of pure ${}_{58}{}^{144}\text{Ce}$ is about 40 times greater than the activity of the same amount of pure ${}_{55}{}^{137}\text{Cs}$.

Discuss which of the two nuclides is more likely to require long-term storage once removed from the reactor.

Every neutron-induced fission reaction of uranium-235 releases an energy of about 200 MeV. A nuclear power station transfers an energy of about 2.4 GJ per second.

Determine the mass of uranium-235 that undergoes fission in one day in this power station.

Every neutron-induced fission reaction of uranium-235 releases an energy of about 200 MeV. A nuclear power station transfers an energy of about 2.4 GJ per second.

Determine the mass of uranium-235 that undergoes fission in one day in this power station.

Two radioactive samples $\mathrm{X}$ and $\mathrm{Y}$ have the same half-life. Initially the ratio $\frac{\mathrm{activity} \mathrm{of} \mathrm{X}}{\mathrm{activity} \mathrm{of} \mathrm{Y}}$ is 4.

What is this ratio after 2 half-lives?

A.  $\frac{1}{2}$

B.  1

C.  2

D.  4

Two radioactive samples $\mathrm{X}$ and $\mathrm{Y}$ have the same half-life. Initially the ratio $\frac{\mathrm{activity} \mathrm{of} \mathrm{X}}{\mathrm{activity} \mathrm{of} \mathrm{Y}}$ is 4.

What is this ratio after 2 half-lives?

A.  $\frac{1}{2}$

B.  1

C.  2

D.  4

Calculate the maximum current in the chamber due to the electrons when there is no smoke in the chamber.