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An alpha particle of mass m undergoes 1 D elastic collision with a stationary nuclei and bounces back losing 64% of its kinetic energy. Find mass of nuclie.... . .. .... . .. . Please provide complete solution

An alpha particle of mass m undergoes 1 D elastic collision with a stationary nuclei and bounces back losing 64% of its kinetic energy. Find mass of nuclie.... . .. .... . .. . Please provide complete solution

Grade:12th pass

1 Answers

Khimraj
3007 Points
5 years ago
64% = 16/25
let mass of stationary nuclei = x
u1,  u2=0
1/2 m * v1^2 = 16/25 * 1/2 x * u1^2    =>  v1 = 4 u1 /5
Assuming that there is no effect due to the particle being electrically charged. We assume that the collision is elastic.
Conservation of linear momentum:
      m u1 + x u2 = m v1 + x v2
      m u1 = m *4 u1 / 5 + x  v2
      x v2 = m u1 /5         --- (1)
Conservation of energy:
      1/2 m u1^2 + 1/2 x u2^2 = 1/2 m v1^2 + 1/2 x v2^2
      x v2^2 = 9/25 m  u1^2      -- (2)
(2) / (1)  =>   v2 = 9/5 * u1
Substitute in (1) to get:    x/m = 1/9
x = m/9
Hope it clears.......................................

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