| Date | November 2014 | Marks available | 2 | Reference code | 14N.3.HL.TZ0.19 |
| Level | Higher level | Paper | Paper 3 | Time zone | Time zone 0 |
| Command term | Calculate | Question number | 19 | Adapted from | N/A |
Question
This question is about relativistic momentum and energy.
An electron and a positron travel towards each other in a straight line in a vacuum. A positron is a positively charged electron.
The speed of each particle, as measured by an observer in the laboratory, is 0.85c. The value of the Lorentz factor at this speed is approximately 1.9.
The electron and positron annihilate each other, creating two photons in the process. Each of the photons transfers the same quantity of energy.
Calculate the speed of the positron as measured in the frame of reference of the electron.
Calculate the total energy in the reaction.
Outline why two photons must be released in this collision.
Determine the frequency of one of the photons.
Markscheme
\({u'_x} = \frac{{{u_x} - v}}{{1 - \frac{{{u_x}v}}{{{c^2}}}}} = \frac{{0.85{\text{c}} - [ - 0.85{\text{c]}}}}{{1 + {{[0.85]}^2}}}\);
0.99c;
\(E = \left( {2[\gamma {m_0}{c^2}] = 2 \times 1.9 \times 0.511 = } \right){\text{ }}1.94{\text{ MeV}}\)\(\,\,\,\)or\(\,\,\,\)\(3.1 \times {10^{ - 13}}{\text{ J}}\);
total momentum before the collision is zero;
if only one photon is emitted then the total momentum after the collision cannot be zero, otherwise momentum will not be conserved;
\(f = \frac{E}{h} = \frac{{0.5 \times 1.9418 \times {{10}^6} \times 1.6 \times {{10}^{ - 19}}}}{{6.63 \times {{10}^{ - 34}}}}\) ; (allow ECF from (b)(i))
\(f = 2.3 \times {10^{20}}{\text{ Hz }}\);
Examiners report
Well prepared candidates showed a good ability to apply relativistic velocity addition. (b) discriminated well.
Well prepared candidates showed a good ability to apply relativistic velocity addition. (b) discriminated well.
Well prepared candidates showed a good ability to apply relativistic velocity addition. (b) discriminated well.
Well prepared candidates showed a good ability to apply relativistic velocity addition. (b) discriminated well.
