| Date | May 2011 | Marks available | 3 | Reference code | 11M.3.HL.TZ2.15 |
| Level | Higher level | Paper | Paper 3 | Time zone | Time zone 2 |
| Command term | Calculate | Question number | 15 | Adapted from | N/A |
Question
This question is about relativistic mechanics.
Calculate the potential difference through which a proton, starting from rest, must be accelerated for its mass–energy to be equal to three times its rest mass energy.
[3]
a.
Calculate the momentum of the proton after acceleration.
[3]
b.
Markscheme
3mpc2 = kinetic energy gain+mpc2 ;
kinetic energy gain = 2×938c2(MeVc−2);
1900MV;
a.
9mp2c4=p2c2+mp2c4;
p2c2=8mp2c4;
p=2700MeVc−1;
or
γ=3;
to give v=0.943c;
p=γmpv=3×938×0.943=2700MeVc−1;
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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