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In case of head on collision, when the impact parameter is minimum, θ= _____ rad (where θ = scattering angle for α-particle)

Asked in GSEB Board March 2020 · Rutherford's model and its limits

• (1) 0
• (2) π/2
• (3) π/4
• (4) π

Step-by-step solution

Why the other options are wrong

• (1) 0 is the scattering angle for a very large impact parameter, where the particle passes far from the nucleus and carries straight on; a head-on approach is the opposite extreme.
• (2) π/2 is θ/2, not θ: setting cot θ/2=0 gives θ/2=π/2, and the question asks for θ itself.
• (3) comes from no single slip produces π/4. Sanity check: b=0 forces cot θ/2=0, so θ/2=π/2 and θ=π.

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