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Q.43 - Excercises And Problems

Expert-verified
Found in: Page 1118

### Physics for Scientists and Engineers: A Strategic Approach with Modern Physics

Book edition 4th
Author(s) Randall D. Knight
Pages 1240 pages
ISBN 9780133942651

# Heavy nuclei often undergo alpha decay in which they emit an alpha particle (i.e., a helium nucleus). Alpha particles are so tightly bound together that it's reasonable to think of an alpha particle as a single unit within the nucleus from which it is emitted.a. nucleus, which decays by alpha emission, is in diameter. Model an alpha particle within nucleus as being in a onc-dimensional box. What is the maximum specd an alpha particle is likely to have?b. The probability that a nucleus will undergo alpha decay is proportional to the frequency with which the alpha particle reflects from the walls of the nucleus. What is that frequency (reflections/s) for a maximum-speed alpha particle within a nucleus?

(a) Thus, the maximum speed of an alpha particle is from

(b) The frequency for a maximum speed of an alpha particle within the nucleus is

See the step by step solution

## Part (a) Step 1: Given Information

Diameter of an alpha emission

## Part (a) Step 2: solution

(a) The velocity is calculated from eq(1)

Applying and

Thus, the velocity within the interval is

The velocity is

Conclusion:Thus, the maximum speed of an alpha particle is from 0 to .

## Part (b) Step 1: Given Information

The frequency for maximum speed of an alpha particle within the nucleus is calculated from the formula,

## Part (b) Step 2: solution

Applying vx and

Conclusion:The frequency for a maximum speed of an alpha particle within the nucleus is