Q. A alpha nucleus of energy (1/2)mv² bombards a heavy nuclear target of charge Ze. Then the distance of closest approach for the alpha nucleus will be proportional to
A) 1/v⁴
B) 1/(Ze)
C) v²
D) 1/m
Explanation
[Solution from source] At closest approach all kinetic energy becomes potential energy: ½mv² = (1/4πε₀)(Ze)(2e)/r₀, so r₀ = 4Ze²/(4πε₀mv²). Thus r₀ ∝ 1/m, ∝ Ze and ∝ 1/v², so 1/v⁴ and v² are wrong powers and 1/(Ze) has the wrong dependence. Answer (4).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.