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Date May 2011 Marks available 4 Reference code 11M.2.HL.TZ2.12
Level Higher level Paper Paper 2 Time zone Time zone 2
Command term Explain Question number 12 Adapted from N/A

Question

Photoelectric effect and de Broglie wavelength

The diagram is a representation of apparatus used to study the photoelectric effect.

Light from the monochromatic source is incident on a cathode placed in an evacuated tube. A variable voltage supply is connected between anode and cathode and the photoelectric current is registered by the microammeter. The sketch graph shows how the photoelectric current I varies with the potential difference V between anode and cathode for two sources of light, A and B, of different frequencies and intensities.

Explain with reference to the Einstein model, which graph, A or B, corresponds to the light with the greater frequency.
[4]
a.
The frequency of the light that produces graph A is 8.8×1014Hz. The magnitude of VA is 1.6V.
 
(i)  State the value of the maximum energy, in eV, of the electrons emitted from the cathode.
 
(ii)  Determine the work function, in eV, of the surface of the cathode.
[3]
b.

The frequency of the incident light is increased but the intensity remains constant. Explain why this increase in frequency results in a change to the maximum photoelectric current (saturation current).

[3]
c.

The electrons emitted from the photo-cathode have an associated de Broglie wavelength. Describe what is meant by the de Broglie wavelength.

[2]
d.

Markscheme

Look for these main points.
light consists of photons whose energy depends on the frequency/hf;
hence the energy available to the (photo)electrons will depend on f;
the potentials VA and VB correspond to/are a measure of the maximum kinetic of the emitted electrons;
the work function (of metal)/energy to emit electron is same for both light sources;

as electrons in A have more kinetic energy available, this frequency must be higher;
(so A)

a.

(i) 1.6 eV ; (answer must be expressed in eV)

(ii) energy of photons = \(\left( {\frac{{6.6 \times {{10}^{ - 34}} \times 8.8 \times {{10}^{14}}}}{{1.6 \times {{10}^{ - 19}}}} = } \right)3.6\left( {{\rm{eV}}} \right)\);
work function=(3.6−1.6=) 2.0eV;
Allow answer in J if (b)(i) expressed in joule (ECF), otherwise award [1 max].

b.

photon energy increases (because frequency increases);
so for same intensity fewer photons per second;
so current reduced / fewer electrons emitted per second;

c.

all particles/electrons exhibit wave properties/have an associated wavelength (called the de Broglie wavelength);
the wavelength is equal to the Planck constant divided by the momentum of the particle/electron/ \(\lambda  = \frac{h}{p}\) with terms defined; { (terms must be defined for mark)

d.

Examiners report

Marks were very poor here. It was a rare candidate who explained the answer “with reference to the Einstein model” as requested. There was only a spasmodic mention of the role of the photon or its energy. Many candidates demonstrated misunderstandings about the effect itself. Some thought that electrons arrive and photons are emitted; this was a disturbingly common misapprehension. Consequently it was difficult to award marks.
a.

i) This was commonly correct but often expressed in joule rather than eV as demanded by the question.

(ii) Again, units were often inappropriate but credit was given if the earlier unit in (b)(i) was incorrect. Many were able to manipulate Einstein’s equation with ease.

b.

Almost all candidates suggested that, in the photoelectric effect, when the frequency of incident light increases but the intensity remains constant, then the maximum emitted current increases. They neglected the dependence of the energy of the photon on its frequency. This is further evidence of the lack of understanding by candidates with this area of the syllabus.

c.

Candidates often described what the de Broglie wavelength is, or gave an equation for it, but rarely both (as the markscheme and the mark allocation required).

d.

Syllabus sections

Additional higher level (AHL) » Topic 12: Quantum and nuclear physics » 12.1 – The interaction of matter with radiation
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