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Date November 2013 Marks available 3 Reference code 13N.3.HL.TZ0.13
Level Higher level Paper Paper 3 Time zone Time zone 0
Command term Calculate and Describe Question number 13 Adapted from N/A

Question

This question is about relativistic energy and momentum.

A proton is accelerated from rest through a potential difference V. After acceleration the mass of the proton is equal to four times its rest mass. Determine the value of V.

[3]
a.

For the proton in (a) calculate, after acceleration, its

(i) speed.

(ii) momentum.

[3]
b.

Markscheme

\(V = \left[ {\gamma  - 1} \right]938 \times {10^6}\);
γ=4;
V=(3×938×106=)2.81×109 (V) or 2.81 (GV);

or

eV=[γ –1]mc2;
γ=4;
\(V = \left( {\frac{{3 \times 1.67 \times {{10}^{ - 27}} \times 9 \times {{10}^{16}}}}{{1.6 \times {{10}^{ - 19}}}}} \right) = 2.81 \times {10^9}\left( {\rm{V}} \right)\);
Award [3] for a bald correct answer.

a.

(i) recognize that \(4 = \frac{1}{{\sqrt {1 - \frac{{{v^2}}}{{{c^2}}}} }}\);
to give v=0.968c or 2.90×108(ms–1);
Allow [2 max] ECF for wrong γ taken from (a).
Award [2] for a bald correct answer.

(ii) \(p = \left( {\gamma {m_0}v = } \right)1.9 \times {10^{ - 18}}\left( {{\rm{kgm}}{{\rm{s}}^{ - 1}}} \right)\) or 3.63×103(MeVc-1) or 3.63(GeVc-1);
Watch for ECF from (a) or (b)(i).

b.

Examiners report

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

Syllabus sections

Option A: Relativity » Option A: Relativity (Additional higher level option topics) » A.4 – Relativistic mechanics (HL only)
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