Question

In the Rutherford scattering experiment, the number of alpha particles scattered at an angle $\theta=60^{\circ}$ is 36 per minute. The number of alpha particles per minute scattered at angles $\theta=90^{\circ}$ is (Assume all other conditions to be identical.) (a) 144 (b) 9 (c) 36 (d) 16

Name: Problem 31, Chapter 13: Advanced Problems in Physical Chemistry for Competitive Examinations
Uploaded: 2021-10-05T01:24:42-08:00
Duration: 2 min 4 s
Channel: Farhana Sharmin
Description: In the Rutherford scattering experiment, the number of alpha particles scattered at an angle θ=60^∘ is 36 per minute. The number of alpha particles per minute scattered at angles θ=90^∘ is (Assume all other conditions to be identical.) (a) 144 (b) 9 (c) 36 (d) 16

   In the Rutherford scattering experiment, the number of alpha particles scattered at an angle $\theta=60^{\circ}$ is 36 per minute. The number of alpha particles per minute scattered at angles $\theta=90^{\circ}$ is (Assume all other conditions to be identical.)
(a) 144
(b) 9
(c) 36
(d) 16

Advanced Problems in Physical Chemistry for Competitive Examinations

Neeraj Kumar 2015 Edition

Chapter 13, Problem 31

Instant Answer

Solved by Expert Farhana Sharmin

10/05/2021

Step 1

This can be written as: \[N \propto \frac{1}{\sin^{4}(\theta/2)}\] Show more…

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In the Rutherford scattering experiment, the number of alpha particles scattered at an angle $\theta=60^{\circ}$ is 36 per minute. The number of alpha particles per minute scattered at angles $\theta=90^{\circ}$ is (Assume all other conditions to be identical.) (a) 144 (b) 9 (c) 36 (d) 16

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Key Concepts

Rutherford Scattering Theory

This theory describes how charged particles, such as alpha particles, are deflected by the Coulomb force when they approach a nucleus. A key result of this theory is the differential cross section, which quantifies the probability of scattering into a particular solid angle and is derived from Coulomb’s law.

Differential Cross Section and Angular Dependence

In Rutherford scattering, the differential cross section is proportional to 1/(sin?(?/2)). This means that the number of particles scattered at an angle depends very sensitively on the scattering angle ?. As the scattering angle increases, the value of sin(?/2) increases, leading to a rapid decrease in the scattering cross section and hence in the number of particles scattered in that particular direction.

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