solutions 01

# Introductory Nuclear Physics

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PHY431 Homework Set 1 Reading: Lecture Notes Homework: See below Due date: Monday Jan 23 Problems, Hints and Solutions Problem I.1 Special Relativity Muons are produced in upper atmosphere air showers initiated by high-energy cosmic rays (mostly protons). Muons have a lifetime of 2.1 μ s (i.e. their mean life in their own restframe). Calculate the relativistic factor γ≡ 1 / (1 - β ²) , where β≡ v / c , for a muon with speed v = 0.98 c . . The mass of a muon is 105 MeV. Calculate the energy and momentum of a muon with v = 0.98 c . b. Calculate the distance the muon travels for an earth-based observer (who sees the muon speeding by with v = 0.98 c ). c. What fraction of muons with v = 0.98 c and produced at 5.0 km above sea-level will reach sea-level? d. Multiple choice: I see two muons pass by with equal speed; one muon just newly produced (age 0 μ s), and another muon that is already "old" (having lived for several μ s). Which of the two muons is most likely to decay first: i. The youngest muon ii. The older muon iii. Both are equally likely.

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