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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.

[1]
a.i.

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.

[1]
a.ii.

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.

[2]
b.i.

Discuss how your result in (b)(i) and the outcome of the muon decay experiment support the theory of special relativity.

[2]
b.ii.

Markscheme

«\(\frac{{{{10}^4}}}{{0.995 \times 3 \times {{10}^8}}} = \)» 34 «μs»

 

Do not accept 104/c = 33 μs.

[1 mark]

a.i.

time is much longer than 10 times the average life time «so only a small proportion would not decay»

[1 mark]

a.ii.

\(\gamma  = 10\)

\(\Delta {t_0} = \) «\(\frac{{\Delta t}}{\gamma } = \frac{{34}}{{10}} = \)» 3.4 «μs»

[2 marks]

b.i.

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]

b.ii.

Examiners report

[N/A]
a.i.
[N/A]
a.ii.
[N/A]
b.i.
[N/A]
b.ii.

Syllabus sections

Option A: Relativity » Option A: Relativity (Core topics) » A.2 – Lorentz transformations
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