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Date May 2012 Marks available 4 Reference code 12M.3.HL.TZ2.15
Level Higher level Paper Paper 3 Time zone Time zone 2
Command term Determine Question number 15 Adapted from N/A

Question

This question is about mass and energy.

The graph shows the variation with the fraction \(\frac{v}{c}\), of the kinetic energy EK of a particle, where v is the speed of the particle.

Determine, using the value EK =360 MeV from the graph, the rest mass of the particle in MeV c–2.

[4]
a.

Determine, using data from the graph, the potential difference required to accelerate the particle in (a) from a speed of 0.63c to a speed of 0.96c. The charge of the particle is +e.

[2]
b.

Markscheme

v=0.96c when EK=360(MeV);

calculation of gamma factor \(\gamma  = \frac{1}{{\sqrt {1 - {{0.96}^2}} }} = 3.571\);
so that \(m = \frac{{{E_{\rm{K}}}}}{{\left( {\gamma  - 1} \right){c^2}}} = \frac{{360}}{{2.571{{\rm{c}}^2}}}\);
m=140MeVc-2;

a.

change in kinetic energy is 360-40 = 320MeV;
so voltage required is 320MV ; (unit needed) 
MV needed for second marking point.

b.

Examiners report

 

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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