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Question 18M.3.SL.TZ1.4

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Date May 2018 Marks available [Maximum mark: 6] Reference code 18M.3.SL.TZ1.4
Level SL Paper 3 Time zone TZ1
Command term Calculate, Deduce, Discuss Question number 4 Adapted from N/A
4.
[Maximum mark: 6]
18M.3.SL.TZ1.4

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.

(a.i)

Calculate, according to Galilean relativity, the time taken for a muon to travel to the ground.

[1]

Markscheme

« 10 4 0.995 × 3 × 10 8 = » 34 «μs»

 

Do not accept 104/c = 33 μs.

[1 mark]

(a.ii)

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]

Markscheme

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

[1 mark]

(b.i)

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]

Markscheme

γ = 10

Δ t 0 =  « Δ t γ = 34 10 = » 3.4 «μs»

[2 marks]

(b.ii)

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

[2]

Markscheme

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]

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