An alpha nucleus of energy ½mv² bombards a heavy nuclear target of charge Ze. Then the distance of closest approach for the alpha nucleus will be proportional to:
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Question

An alpha nucleus of energy ½mv² bombards a heavy nuclear target of charge Ze. Then the distance of closest approach for the alpha nucleus will be proportional to:

G1 Physics · Accepted Answer

At closest approach the α-particle kinetic energy converts into Coulomb potential energy: ½mv² = (1/(4πε₀))(2Ze²)/rₘᵢₙ. Hence rₘᵢₙ = 4Ze²/(4πε₀mv²). For fixed projectile speed and target Z, rₘᵢₙ ∝ 1/m, corresponding to option C. Answer: C.