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Q.43 - Excercises And Problems

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 1118

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Short Answer

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

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

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