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The distance of the closest approach of an alpha particle fired at a nucleus with kinetic energy K is r₀. The distance of the closest approach when the α particle is fired at the same nucleus with kinetic energy 2K will be

Asked in GUJCET 2015 · Distance of closest approach

• (1) 4r₀
• (2) (r₀)/2
• (3) (r₀)/4
• (4) 2r₀

Step-by-step solution

Why the other options are wrong

• (1) comes from no single slip produces 4r₀: since r₀∝1/K, doubling the energy can only bring the particle closer. Sanity check: the new distance is (r₀)/2.
• (3) (r₀)/4 takes the closest approach as falling with the square of the energy, r₀∝1/(K²); it falls only as 1/K.
• (4) 2r₀ makes the distance grow with the energy, r₀∝ K; a faster particle gets closer to the nucleus, not further away.

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