Quantum Physics: Physics 9702 (Cambridge International AS & A Level)

A helium-neon laser used in a college physics laboratory emits red light of wavelength $632.8\text{ nm}$.

What is the energy of one photon of this light, in electron-volts (eV)?

A photocell contains a caesium metal surface with work function $\phi = 2.14\text{ eV}$, housed inside an evacuated glass tube.

(a) State what is meant by the work function of a metal. [1]

(b) Show that the threshold frequency for photoelectric emission from this caesium surface is $f_0 = 5.16\times10^{14}\text{ Hz}$. [2]

(c) The caesium surface is now illuminated with violet light of wavelength $380\text{ nm}$. Calculate the maximum kinetic energy of the photoelectrons emitted, giving your answer in both joules and electron-volts. [3]

(d) Calculate the maximum speed of these photoelectrons. (mass of electron $= 9.11\times10^{-31}\text{ kg}$) [2]

(e) The intensity of the violet light is now increased, while its frequency is kept the same. State and explain the effect, if any, of this change on (i) the photoelectric current, and (ii) the maximum kinetic energy of the emitted photoelectrons. [2]

In an electron diffraction tube, electrons are accelerated from rest through a potential difference of $U = 2.50\text{ kV}$ before striking a thin sheet of graphite.

(a) Show that the kinetic energy gained by each electron is $4.00\times10^{-16}\text{ J}$. [2]

(b) Calculate the momentum of an electron after acceleration. (mass of electron $=9.11\times10^{-31}\text{ kg}$) [2]

(c) Calculate the de Broglie wavelength of the accelerated electrons. [2]

(d) Beyond the graphite sheet, a pattern of concentric rings is observed on a fluorescent screen. State what this observation demonstrates about electrons, and explain briefly why this cannot be accounted for using a simple particle model of the electron. [2]

An isolated atom of a certain gas has three relevant electron energy levels: $E_1=-5.60\text{ eV}$ (the ground state), $E_2=-3.10\text{ eV}$, and $E_3=-1.20\text{ eV}$.

(a) Explain what is meant by stating that the electron energies of the atom are quantised. [1]

(b) An electron in the atom makes a transition from level $E_3$ to level $E_1$, emitting a photon. Calculate the energy of the emitted photon, giving your answer in both electron-volts and joules. [2]

(c) Calculate the frequency and the wavelength of this emitted photon, and state which region of the electromagnetic spectrum it lies in. [3]

(d) The atom is now in its ground state $E_1$. A beam of white light, containing a continuous range of wavelengths, is passed through a sample of this gas. Explain, in terms of photon absorption, how dark absorption lines can appear in the transmitted spectrum. [2]

A photon has energy $E=3.00\text{ eV}$.

What is the magnitude of the momentum of this photon?

In an electron gun, an electron travels with speed $v=2.00\times10^{6}\text{ m s}^{-1}$.

What is the de Broglie wavelength of this electron? (mass of electron $=9.11\times10^{-31}\text{ kg}$)

A clean sodium surface has work function $\phi=2.30\text{ eV}$.

(a) Show that the threshold wavelength for photoelectric emission from this surface is $540\text{ nm}$. [2]

(b) The surface is illuminated with violet light of wavelength $400\text{ nm}$. State, with a reason, whether photoelectrons are emitted from the surface. [1]

(c) Calculate the maximum kinetic energy of the photoelectrons emitted at $400\text{ nm}$, giving your answer in both joules and electron-volts. [3]

(d) Calculate the stopping potential required to reduce the photoelectric current from this surface to zero. [2]

An isolated atom of a certain gas has two relevant electron energy levels: $E_1=-8.20\text{ eV}$ (the ground state) and $E_2=-3.00\text{ eV}$. A ground-state atom absorbs a photon, exciting an electron from $E_1$ to $E_2$.

What is the wavelength of the absorbed photon?

An electron and a proton are each accelerated from rest through the same potential difference $U=500\text{ V}$.

(a) Show that the kinetic energy gained by each particle is $8.00\times10^{-17}\text{ J}$. [1]

(b) Calculate the momentum of the electron after acceleration. (mass of electron $=9.11\times10^{-31}\text{ kg}$) [2]

(c) Calculate the momentum of the proton after acceleration. (mass of proton $=1.67\times10^{-27}\text{ kg}$) [2]

(d) Calculate the de Broglie wavelength of the electron and of the proton. [2]

(e) Without further calculation, state and explain why the proton's de Broglie wavelength is smaller than the electron's, even though both particles have the same kinetic energy. [2]

In an experiment on the photoelectric effect, light of various frequencies $f$ is shone on a metal photocathode, and the stopping potential $V_s$ needed to reduce the photocurrent to zero is measured for each frequency. A graph of $V_s$ (on the $y$-axis) against $f$ (on the $x$-axis) is a straight line, with gradient $4.14\times10^{-15}\text{ V s}$ and a $y$-intercept of $-1.90\text{ V}$.

(a) Starting from Einstein's photoelectric equation, $hf=\phi+\tfrac12mv_{max}^2$, and the definition of stopping potential, show that $V_s=\left(\dfrac{h}{e}\right)f-\dfrac{\phi}{e}$. [2]

(b) Use the gradient of the graph to determine a value for the Planck constant $h$. [2]

(c) Use the $y$-intercept of the graph to determine the work function $\phi$ of the photocathode, giving your answer in both electron-volts and joules. [2]

(d) Calculate the threshold frequency $f_0$ of the photocathode. [2]