E.1 Structure of the atom

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.

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.

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.

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

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 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.  $\frac{3}{4}\times \frac{E_0}{h}$

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.  $\frac{3}{4}\times \frac{E_0}{h}$

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.  $\frac{3}{4}\times \frac{E_0}{h}$

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

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

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

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 the emission spectrum of an atom.

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

The diagram shows the emission spectrum of an atom.

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

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

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

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.  $155$

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.  $155$

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.  $\frac{hc}{E_4}-\frac{hc}{E_3}$ 

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.  $\frac{hc}{E_4}-\frac{hc}{E_3}$ 

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.

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.

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.  $8{\rho }_{\text{X}}$

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

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

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

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

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

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

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

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

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

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

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

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.

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.

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).

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).

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).