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Date May 2015 Marks available 2 Reference code 15M.3.SL.TZ1.5
Level Standard level Paper Paper 3 Time zone Time zone 1
Command term Calculate Question number 5 Adapted from N/A

Question

This question is about the photoelectric effect and the de Broglie hypothesis.

When photons are incident on a lithium surface photoelectrons are emitted. The work function φ of lithium is 2.9 eV.

Define work function.

[1]
a.

Determine the maximum wavelength of the photons that can cause photoemission.

[2]
b.

Calculate the momentum of an electron that has the same de Broglie wavelength as the wavelength of the photons in (b).

[2]
c.

Markscheme

minimum energy/work required to remove an electron (from the surface of the substance);

a.

\({f_{\min }} = \frac{{2.9 \times 1.6 \times {{10}^{ - 19}}}}{{6.63 \times {{10}^{ - 34}}}} = \left( {7.0 \times {{10}^{14}}} \right)\left( {{\text{Hz}}} \right)\);

\({\lambda _{\max }} = \left( {\frac{{3.00 \times {{10}^8}}}{{7.0 \times {{10}^{14}}}}} \right) = 4.3 \times {10^{ - 7}}\left( {\text{m}} \right)\);

b.

\(p = \left( {\frac{h}{{{\lambda _{\max }}}} = } \right)\frac{{6.63 \times {{10}^{ - 34}}}}{{4.3 \times {{10}^{ - 7}}}}\);
=
1.5×10-27 (kg ms-1);
Allow ECF from (b).

or

\(p = \left( {\frac{\phi }{c} = } \right)\frac{{2.9 \times 1.6 \times {{10}^{ - 19}}}}{{3.00 \times {{10}^8}}}\)
=
1.5×10-27 (kg ms-1);
Allow ECF from (b).

c.

Examiners report

[N/A]
a.
[N/A]
b.
[N/A]
c.

Syllabus sections

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