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Date May 2011 Marks available 2 Reference code 11M.3.SL.TZ2.4
Level Standard level Paper Paper 3 Time zone Time zone 2
Command term Explain Question number 4 Adapted from N/A

Question

This question is about the de Broglie hypothesis.

State the de Broglie hypothesis.

[2]
a.

Determine the de Broglie wavelength of a proton that has been accelerated from rest through a potential difference of 1.2 kV.

[2]
b.

Explain why a precise knowledge of the de Broglie wavelength of the proton implies that its position cannot be observed.

[2]
c.

Markscheme

particles have an associated wavelength;
wavelength=\(\frac{h}{{mv}}\) or \(\frac{h}{{p}}\); (symbols must be defined)

a.

\(\lambda  = \frac{h}{{\sqrt {2{\rm{meV}}} }}\);
8.3×10−13m;

b.

(Heisenberg suggests that) ΔpΔx is a constant or \( \ge \frac{h}{{4\pi }}\);
if λ is known then Δp is zero therefore uncertainty in position Δx is infinite/very large;
Award [1 max] if Δp and Δx not defined.

or

(the Uncertainty Principle states that) it is impossible to know the position and momentum of a particle at the same time;
if λ is precise then momentum is precise so position is not known;

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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