| Date | May 2018 | Marks available | 2 | Reference code | 18M.3.SL.TZ1.4 |
| Level | Standard level | Paper | Paper 3 | Time zone | Time zone 1 |
| Command term | Calculate | Question number | 4 | Adapted from | N/A |
Question
Muons are created in the upper atmosphere of the Earth at an altitude of 10 km above the surface. The muons travel vertically down at a speed of 0.995c with respect to the Earth. When measured at rest the average lifetime of the muons is 2.1 μs.
Calculate, according to Galilean relativity, the time taken for a muon to travel to the ground.
Deduce why only a small fraction of the total number of muons created is expected to be detected at ground level according to Galilean relativity.
Calculate, according to the theory of special relativity, the time taken for a muon to reach the ground in the reference frame of the muon.
Discuss how your result in (b)(i) and the outcome of the muon decay experiment support the theory of special relativity.
Markscheme
«\(\frac{{{{10}^4}}}{{0.995 \times 3 \times {{10}^8}}} = \)» 34 «μs»
Do not accept 104/c = 33 μs.
[1 mark]
time is much longer than 10 times the average life time «so only a small proportion would not decay»
[1 mark]
\(\gamma = 10\)
\(\Delta {t_0} = \) «\(\frac{{\Delta t}}{\gamma } = \frac{{34}}{{10}} = \)» 3.4 «μs»
[2 marks]
the value found in (b)(i) is of similar magnitude to average life time
significant number of muons are observed on the ground
«therefore this supports the special theory»
[2 marks]
