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KCET2024PhysicsAtomic Physics

In alpha particle scattering experiment, if v is the initial velocity of the particle, then the distance of closest approach is d . If the velocity is doubled, then the distance of closest approach changes to:

Options

  1. A4 d
  2. B2 d
  3. Cd 2
  4. Dd 4

Correct answer

D. d 4

Step-by-step solution

If r₀ be the distance of closest approach, then ( KE )_ = (Z e)(2 e) 4 ₀ (r₀ )_ 1 2 m v_ ^2= (Z e)(2 e) 4 ₀ (r₀ )_ v_ ^2 1 (r₀ )_ (r₀ )_ 1 v_ ^2 (r₀ )_ _i (r₀ )_ _f = v_ _f ^2 v_ i ^2 = (2 v_ _i )^2 v_ _i ^2 =4 (r₀ )_ _f = (r₀ ) _i 4 = d 4 [ (r₀ )_ _i =d ]

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