12.1 – The interaction of matter with radiation

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.

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.

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.

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

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

A particle of energy $E$ is incident upon a barrier and has a certain probability of quantum tunnelling through the barrier. Assuming $E$ remains constant, which combination of changes in particle mass and barrier length will increase the probability of the particle tunnelling through the barrier?

A particle of energy $E$ is incident upon a barrier and has a certain probability of quantum tunnelling through the barrier. Assuming $E$ remains constant, which combination of changes in particle mass and barrier length will increase the probability of the particle tunnelling through the barrier?

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.  $4f$

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.  $4f$

Suggest, with reference to conservation of energy, how the variable voltage source can be used to stop all emitted electrons from reaching the collecting plate.

Suggest, with reference to conservation of energy, how the variable voltage source can be used to stop all emitted electrons from reaching the collecting plate.

Suggest, with reference to conservation of energy, how the variable voltage source can be used to stop all emitted electrons from reaching the collecting plate.

Show that the energy of photons from the UV lamp is about 10 eV.

Show that the energy of photons from the UV lamp is about 10 eV.

Show that the energy of photons from the UV lamp is about 10 eV.

Using the answer in (b) and (c)(i), deduce that the radius r of the electron’s orbit in the ground state of hydrogen is given by the following expression.

$$r=\frac{h^2}{4{\pi }^{2}k{m}_{\text{e}}{e}^2}$$

Using the answer in (b) and (c)(i), deduce that the radius r of the electron’s orbit in the ground state of hydrogen is given by the following expression.

$$r=\frac{h^2}{4{\pi }^{2}k{m}_{\text{e}}{e}^2}$$

Using the answer in (b) and (c)(i), deduce that the radius r of the electron’s orbit in the ground state of hydrogen is given by the following expression.

$$r=\frac{h^2}{4{\pi }^{2}k{m}_{\text{e}}{e}^2}$$

Calculate the electron’s orbital radius in (c)(ii).

Calculate the electron’s orbital radius in (c)(ii).

Calculate the electron’s orbital radius in (c)(ii).

A beam of electrons moving in the direction shown is incident on a rectangular slit of width $d$.

The component of momentum of the electrons in direction $y$ after passing through the slit is $p$. The uncertainty in $p$ is

A.  proportional to $d$

B.  proportional to $\frac{1}{d}$

C.  proportional to $\frac{1}{d^2}$

D.  zero

A beam of electrons moving in the direction shown is incident on a rectangular slit of width $d$.

The component of momentum of the electrons in direction $y$ after passing through the slit is $p$. The uncertainty in $p$ is

A.  proportional to $d$

B.  proportional to $\frac{1}{d}$

C.  proportional to $\frac{1}{d^2}$

D.  zero

Which graph shows a possible probability density function ${\left|\text{Ψ}\right|}^2=\frac{P\left(r\right)}{\Delta V}$ for a given wave function $\text{Ψ}$ of an electron?

Which graph shows a possible probability density function ${\left|\text{Ψ}\right|}^2=\frac{P\left(r\right)}{\Delta V}$ for a given wave function $\text{Ψ}$ of an electron?

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?

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?

The de Broglie wavelength for an electron is given by $\frac{hc}{E}$. Show that the diameter of an oxygen-16 nucleus is about 4 fm.

The de Broglie wavelength for an electron is given by $\frac{hc}{E}$. Show that the diameter of an oxygen-16 nucleus is about 4 fm.

The de Broglie wavelength for an electron is given by $\frac{hc}{E}$. Show that the diameter of an oxygen-16 nucleus is about 4 fm.

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?

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?

Estimate for $n=3$, the ratio $\frac{\mathrm{circumference} \mathrm{of} \mathrm{orbit}}{\mathrm{de} \mathrm{Broglie} \mathrm{wavelength} \mathrm{of} \mathrm{electron}}$.

State your answer to one significant figure.

Estimate for $n=3$, the ratio $\frac{\mathrm{circumference} \mathrm{of} \mathrm{orbit}}{\mathrm{de} \mathrm{Broglie} \mathrm{wavelength} \mathrm{of} \mathrm{electron}}$.

State your answer to one significant figure.

Estimate for $n=3$, the ratio $\frac{\mathrm{circumference} \mathrm{of} \mathrm{orbit}}{\mathrm{de} \mathrm{Broglie} \mathrm{wavelength} \mathrm{of} \mathrm{electron}}$.

State your answer to one significant figure.

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.

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.

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 de Broglie wavelength $\lambda$ of the electron in the $n=3$ state is  $\lambda =5.1\times {10}^{-10}$ m.

The formula for the de Broglie wavelength of a particle is $\lambda =\frac{h}{mv}$.

Show that the de Broglie wavelength $\lambda$ of the electron in the $n=3$ state is  $\lambda =5.1\times {10}^{-10}$ m.

The formula for the de Broglie wavelength of a particle is $\lambda =\frac{h}{mv}$.

Show that the de Broglie wavelength $\lambda$ of the electron in the $n=3$ state is  $\lambda =5.1\times {10}^{-10}$ m.

The formula for the de Broglie wavelength of a particle is $\lambda =\frac{h}{mv}$.

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

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

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

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

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

The energy released in the decay is of the order of 10⁸ eV.

Estimate, using the uncertainty principle, the mean lifetime of the delta baryon.

The energy released in the decay is of the order of 10⁸ eV.

Estimate, using the uncertainty principle, the mean lifetime of the delta baryon.

The energy released in the decay is of the order of 10⁸ eV.

Estimate, using the uncertainty principle, the mean lifetime of the delta baryon.

Samples of different radioactive nuclides have equal numbers of nuclei. Which graph shows the relationship between the half-life $t_{\frac{1}{2}}$ and the activity A for the samples?

Samples of different radioactive nuclides have equal numbers of nuclei. Which graph shows the relationship between the half-life $t_{\frac{1}{2}}$ and the activity A for the samples?

Two radioactive nuclides, X and Y, have half-lives of 50 s and 100 s respectively. At time t = 0 samples of X and Y contain the same number of nuclei.

What is $\frac{\text{number of nuclei of X undecayed}}{\text{number of nuclei of Y undecayed}}$ when t = 200 s?

A.     4

B.     2

C.     $\frac{1}{2}$

D.     $\frac{1}{4}$

Two radioactive nuclides, X and Y, have half-lives of 50 s and 100 s respectively. At time t = 0 samples of X and Y contain the same number of nuclei.

What is $\frac{\text{number of nuclei of X undecayed}}{\text{number of nuclei of Y undecayed}}$ when t = 200 s?

A.     4

B.     2

C.     $\frac{1}{2}$

D.     $\frac{1}{4}$

The variable voltage can be adjusted so that no electrons reach the collecting plate. Write down the minimum value of the voltage for which no electrons reach the collecting plate.

The variable voltage can be adjusted so that no electrons reach the collecting plate. Write down the minimum value of the voltage for which no electrons reach the collecting plate.

The variable voltage can be adjusted so that no electrons reach the collecting plate. Write down the minimum value of the voltage for which no electrons reach the collecting plate.

Bohr modified the Rutherford model by introducing the condition mvr = n$\frac{h}{2\pi }$. Outline the reason for this modification.

Bohr modified the Rutherford model by introducing the condition mvr = n$\frac{h}{2\pi }$. Outline the reason for this modification.

Bohr modified the Rutherford model by introducing the condition mvr = n$\frac{h}{2\pi }$. Outline the reason for this modification.

A beam of monochromatic radiation is made up of photons each of momentum $p$. The intensity of the beam is doubled without changing frequency. What is the momentum of each photon after the change?

A.  $\frac{p}{2}$

B.  $p$

C.  $2p$

D.  $4p$

A beam of monochromatic radiation is made up of photons each of momentum $p$. The intensity of the beam is doubled without changing frequency. What is the momentum of each photon after the change?

A.  $\frac{p}{2}$

B.  $p$

C.  $2p$

D.  $4p$

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

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

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

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

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

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

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

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

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.  $\frac{h}{e}$

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.  $\frac{h}{e}$

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

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

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

Two surfaces X and Y emit radiation of the same surface intensity. X emits a radiation of peak wavelength twice that of Y.

What is $\frac{\mathrm{emissivity} \mathrm{of} \mathrm{X}}{\mathrm{emissivity} \mathrm{of} \mathrm{Y}}$?

A.  $\frac{1}{16}$

B.  $\frac{1}{2}$

C.  2

D.  16

Two surfaces X and Y emit radiation of the same surface intensity. X emits a radiation of peak wavelength twice that of Y.

What is $\frac{\mathrm{emissivity} \mathrm{of} \mathrm{X}}{\mathrm{emissivity} \mathrm{of} \mathrm{Y}}$?

A.  $\frac{1}{16}$

B.  $\frac{1}{2}$

C.  2

D.  16

Two surfaces X and Y emit radiation of the same surface intensity. X emits a radiation of peak wavelength twice that of Y.

What is $\frac{\mathrm{emissivity} \mathrm{of} \mathrm{X}}{\mathrm{emissivity} \mathrm{of} \mathrm{Y}}$?

A.  $\frac{1}{16}$

B.  $\frac{1}{2}$

C.  2

D.  16

Two surfaces X and Y emit radiation of the same surface intensity. X emits a radiation of peak wavelength twice that of Y.

What is $\frac{\mathrm{emissivity} \mathrm{of} \mathrm{X}}{\mathrm{emissivity} \mathrm{of} \mathrm{Y}}$?

A.  $\frac{1}{16}$

B.  $\frac{1}{2}$

C.  2

D.  16