E.2 Quantum physics

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.  $4$

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.

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

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

Determine the wavelength of the incident photon.

Determine the wavelength of the incident photon.

Determine the wavelength of the incident photon.

Calculate the scattering angle of the photon.

Calculate the scattering angle of the photon.

Calculate the scattering angle of the photon.

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.

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.

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.

State the de Broglie hypothesis.

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.

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.

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.

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.

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.

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.

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

Show that the Compton wavelength is about 2.4 pm.

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

Show that the Compton wavelength is about 2.4 pm.

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.

Outline why the wavelength of the photon has changed.

Outline why the wavelength of the photon has changed.

Deduce the scattering angle for the photon.

Deduce the scattering angle for the photon.

Deduce the scattering angle for the photon.

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

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

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

the work function of the surface, in eV.

the work function of the surface, in eV.

the work function of the surface, in eV.

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

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

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

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

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

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

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.  $\frac{hc}{e}$

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.  $\frac{hc}{e}$

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.  $\frac{hc}{e}$

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.  $\frac{hc}{e}$

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?

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.

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.

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 $3\times {10}^{-15} \mathrm{m}$.

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

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

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

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

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.  $4f$

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 $700 {\text{km\hspace{0.05em}\hspace{0.05em}s}}^{-1}$.

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 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

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?

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?

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?

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?

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?

the work function of the surface, in eV.

the work function of the surface, in eV.

the work function of the surface, in eV.

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

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

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