In an -particle scattering experiment, the distance of closest approach for a head-on collision is r₀ . If an -particle of the same kinetic energy is scattered by an angle of 90^ , what is its impact parameter?

Step-by-step solution

The distance of closest approach r₀ for a head-on collision ( = 180^ ) of an -particle with kinetic energy K is given by equating kinetic energy to electrostatic potential energy: K = 1 4 ₀ (2e)(Ze) r₀ r₀ = 1 4 ₀ 2Ze^2 K The impact parameter b for an -particle scattered at an angle is given by: b = 1 4 ₀ Ze^2 ( /2) K Comparing the two expressions, we can write b in terms of r₀ : b = r₀ 2 ( 2 ) For a scattering angle = 90^ : b = r₀ 2 (45^ ) Since (45^ ) = 1 , we get: b = r₀ 2 Answer: r₀ 2