OCR A-Level Physics: Quantum Physics

When electromagnetic radiation of a high enough frequency is shone onto a clean metal surface in a vacuum, electrons are emitted from the surface almost instantly. Three features of this photoelectric effect cannot be explained by treating light as a continuous wave:

• there is a threshold frequency below which no electrons are emitted, no matter how bright the light;
• the maximum kinetic energy of the emitted electrons depends on the frequency of the light but not on its intensity;
• emission begins as soon as the light reaches the surface, even when the light is very faint.

Explain how each of these three observations supports the photon (particle) model of light and why the wave theory of light fails to account for them.

(6 marks)

A clean sodium surface in a vacuum is illuminated with monochromatic ultraviolet light of wavelength 400 nm. The work function of sodium is given in the table below.

Quantity	Value
Wavelength of light, $\lambda$λ	400 nm
Work function of sodium, $\phi$ϕ	2.28 eV
Planck constant, $h$h	$6.63\times10^{-34}$6.63×10−34 J s
Speed of light, $c$c	$3.00\times10^8$3.00×108 m s⁻¹
Elementary charge, $e$e	$1.60\times10^{-19}$1.60×10−19 C

(a) Show that the energy of one photon of this light is about $5.0\times10^{-19}$5.0×10−19 J. (2 marks)

(b) Calculate the maximum kinetic energy of an emitted photoelectron, in joules. (2 marks)

(c) Hence calculate the stopping potential needed to just prevent these electrons from reaching the collector. (2 marks)

In an experiment a metal surface is illuminated with light of several different frequencies and the maximum kinetic energy of the photoelectrons is measured each time. The results are plotted as a graph of $KE_{\max}$KEmax​ against frequency $f$f, which is a straight line. Selected points read from the line are:

Frequency, $f$f / $10^{14}$1014 Hz	6.0	7.0	8.0	9.0
$KE_{\max}$KEmax​ / $10^{-19}$10−19 J	0.78	1.44	2.10	2.77

Einstein's equation can be written $KE_{\max} = hf - \phi$KEmax​=hf−ϕ.

(a) Use two well-separated points to determine the gradient of the line, and state the physical quantity it represents. (3 marks)

(b) The line crosses the energy axis below zero, at $-3.2\times10^{-19}$−3.2×10−19 J. State what this intercept represents and give the work function of the metal in electronvolts. (2 marks)

In an electron-diffraction tube, electrons are accelerated from rest through a potential difference of 100 V before striking a thin graphite film. The electrons behave as waves and produce a diffraction pattern, confirming the wave nature of matter. (Electron mass $m_e = 9.11\times10^{-31}$me​=9.11×10−31 kg; $e = 1.60\times10^{-19}$e=1.60×10−19 C; $h = 6.63\times10^{-34}$h=6.63×10−34 J s.)

(a) Show that the speed of an electron after acceleration is about $5.9\times10^6$5.9×106 m s⁻¹. (2 marks)

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

(c) Visible-light photons have wavelengths of a few hundred nanometres. State, with a reason, whether visible light or these electrons would reveal more detail about the atomic spacing in the graphite. (1 mark)

A laser pointer emits a continuous beam of red light of wavelength 630 nm with an output power of 5.0 mW. ($h = 6.63\times10^{-34}$h=6.63×10−34 J s; $c = 3.00\times10^8$c=3.00×108 m s⁻¹.)

(a) Calculate the energy of a single photon of this light. (2 marks)

(b) Hence calculate the number of photons the laser emits each second. (2 marks)

The electronvolt is a convenient unit of energy in quantum physics, and the work function of a metal is often quoted in electronvolts.

(a) State what is meant by the work function of a metal surface. (1 mark)

(b) A certain metal has a work function of 2.5 eV. Convert this energy into joules, showing your working. (2 marks)

(Take $e = 1.60\times10^{-19}$e=1.60×10−19 C.)