| 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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