AQA A-Level Physics: Particles, Antiparticles and Quantum Phenomena

When electromagnetic radiation is shone onto a clean metal surface in a vacuum, electrons can be emitted. This is the photoelectric effect. Three experimental observations cannot be explained by treating the incident radiation as a continuous wave:

• below a certain threshold frequency no electrons are emitted, however intense the radiation;
• for radiation above the threshold frequency, electrons are emitted without any measurable time delay, even at very low intensity;
• the maximum kinetic energy of the emitted electrons depends on the frequency of the radiation, not on its intensity.

Explain how each of these three observations supports the photon (particle) model of electromagnetic radiation, and explain why the wave model fails to account for them. Refer to the photon energy $E = hf$E=hf and the work function $\phi$ϕ in your answer.

(6 marks)

In an experiment on the photoelectric effect, monochromatic ultraviolet light of wavelength 380 nm is shone onto the clean surface of a metal whose work function is 2.30 eV.

Quantity	Value
Wavelength of incident light, $\lambda$λ	380 nm
Work function of metal, $\phi$ϕ	2.30 eV
Planck constant, $h$h	$6.63 \times 10^{-34}$6.63×10−34 J s
Speed of light, $c$c	$3.00 \times 10^{8}$3.00×108 m s⁻¹
Elementary charge, $e$e	$1.60 \times 10^{-19}$1.60×10−19 C

(a) Calculate the threshold frequency of the metal. (2 marks)

(b) Show that the energy of an incident photon is about $5.2 \times 10^{-19}$5.2×10−19 J, and hence calculate the maximum kinetic energy of the emitted photoelectrons, in joules. (2 marks)

(c) Calculate the stopping potential required to reduce the photoelectric current to zero. (2 marks)

The diagram below is represented as a table of the lowest four electron energy levels of an isolated atom. Energies are measured in electronvolts relative to the ionised atom (taken as 0 eV).

Level	Energy / eV
$n = 4$n=4	-0.85
$n = 3$n=3	-1.51
$n = 2$n=2	-3.40
$n = 1$n=1 (ground state)	-13.60

When the atoms are excited, electrons drop between levels and emit photons, producing a line emission spectrum. Use $h = 6.63 \times 10^{-34}$h=6.63×10−34 J s, $c = 3.00 \times 10^{8}$c=3.00×108 m s⁻¹ and $1\ \text{eV} = 1.60 \times 10^{-19}$1 eV=1.60×10−19 J.

(a) Calculate the wavelength of the photon emitted when an electron makes the transition from $n = 3$n=3 to $n = 2$n=2. State the region of the electromagnetic spectrum in which this line appears. (3 marks)

(b) One line in the spectrum has a wavelength of 122 nm. Use a calculation to identify the transition that produces this line. (2 marks)

A student is investigating which particle reactions can occur. The three proposed interactions below are written with the relevant quantum numbers available from a data sheet.

Reaction	Equation
A	$\pi^{-} + p \rightarrow K^{0} + \Lambda^{0}$π−+p→K0+Λ0
B	$p + p \rightarrow p + \pi^{+}$p+p→p+π+
C	$n \rightarrow p + e^{-} + \bar{\nu}_e$n→p+e−+νˉe​

For reference: the $\Lambda^{0}$Λ0 is a baryon with strangeness $-1$−1; the $K^{0}$K0 is a meson with strangeness $+1$+1; the $\pi^{-}$π− and $\pi^{+}$π+ have strangeness $0$0.

(a) For each reaction, state with reasons whether it is permitted, by applying the conservation of charge, baryon number, lepton number and strangeness. (4 marks)

(b) Reaction C is mediated by one of the fundamental forces. Name this force and name the exchange particle (gauge boson) responsible. (1 mark)

In an electron-diffraction tube, electrons are accelerated from rest through a potential difference of 2500 V and then strike a thin polycrystalline graphite target, producing a diffraction pattern of concentric rings on a fluorescent screen. The diffraction is evidence of the wave-like behaviour of the electrons.

Quantity	Value
Accelerating potential difference, $V$V	2500 V
Mass of an electron, $m_e$me​	$9.11 \times 10^{-31}$9.11×10−31 kg
Charge of an electron, $e$e	$1.60 \times 10^{-19}$1.60×10−19 C
Planck constant, $h$h	$6.63 \times 10^{-34}$6.63×10−34 J s

(a) Show that the speed of an electron after acceleration is about $3.0 \times 10^{7}$3.0×107 m s⁻¹. Treat the motion as non-relativistic. (2 marks)

(b) Hence calculate the de Broglie wavelength of these electrons. (2 marks)

Protons and neutrons are not fundamental particles: each is a baryon made up of three quarks. In beta-minus ($\beta^{-}$β−) decay a neutron inside an unstable nucleus changes into a proton.

(a) State the quark composition of a proton and of a neutron. (2 marks)

(b) State the change of quark that occurs when a neutron decays into a proton in beta-minus decay. (1 mark)