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Get Answers to all your Questions
(i) Define the terms : ‘impact parameter’ and ‘distance of closest approach’ for an α-particle in Geiger-Marsden scattering experiment.
(ii) What will be the value of the impact parameter for scattering angle (I) θ = 0° and (II) θ = 180°?
Answers (1)
(i) Definitions:
1. Impact Parameter: It is the perpendicular distance between the initial direction of motion of the α-particle and the central line passing through the nucleus of the atom.
2. Distance of Closest Approach: It is the minimum distance between the α-particle and the nucleus during the scattering process, where the entire kinetic energy of the α-particle is converted into electrostatic potential energy.
$\frac{1}{4\pi \varepsilon_0} \frac{2Ze^2}{r_{\min}} = \frac{1}{2} m v^2$
(ii) Values of Impact Parameter:
|
Scattering Angle (θ) |
Value of Impact Parameter (b) |
Explanation |
|---|---|---|
|
θ = 0° |
b → ∞ |
The α-particle passes far away from the nucleus, so it experiences no deflection. |
|
θ = 180° |
b = 0 |
The α-particle moves directly towards the nucleus and is completely repelled backward. |
Final Answer:
-
Impact parameter: shortest perpendicular distance from initial α-particle path to nucleus.
-
Distance of closest approach: minimum separation between α-particle and nucleus.
-
For θ = 0°, b = ∞; for θ = 180°, b = 0.
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