solutions 02

# Introductory Nuclear Physics

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PHY431 Homework Set 2 Reading: Lecture Notes Set 1 Homework: See below Due date: Monday Jan 31 Hints and Solutions Problem II.1 Derive a formula for the minimum kinetic energy K that is necessary for alpha's to just start 'touching the surface' of an atomic nucleus of charge Ze and atomic number A . Assume that the nuclear radius R is related to A as R = R 0 A 1/3 , with R 0 = 1.2×10 -15 m = 1.2 fm. . Calculate this minimum kinetic energy for an Aluminium foil. b. How would one experimentally detect that alphas have started penetrating the nucleus? c. Hints: no hints Solution: The minimum kinetic energy K that is necessary for alpha's to just start 'touching the surface' of an atomic nucleus of charge Ze and atomic number A is reached at impact parameter b =0, and when the initial kinetic energy is momentarily equal to the potential energy when the nuclei touch: K init = zZe ² / (4 πε 0 r ) = 2 Ze ² / (4 πε 0 { R α + R A }) = 2 Ze ² / (4 πε 0 R 0 {2 1/3 + A 1/3 }), with R 0 = 1.2 fm.

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