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

Question

This question is about relativistic energies.

Calculate the speed of an electron when its total energy is equal to five times its rest mass energy.

[3]
a.

The electron is accelerated from rest through a potential difference V. The graph shows how the speed v of the electron after acceleration varies with V assuming that Newtonian mechanics applies.

On the graph, sketch a line to show the variation with V of v according to relativistic mechanics.

[2]
b.

Markscheme

E = \(\gamma \)mc2=5mc2 or \(\gamma \) = 5;
so \(\frac{{{v^2}}}{{{c^2}}} = 1 - 0.04\);
v=0.98c;

 

a.

close to Newton for small v and below Newton for large V; asymptotic to c;

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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