Q.43 - Excercises And ProblemsExpert-verified
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
Diameter of an alpha emission
(a) The velocity is calculated from eq(1)
Thus, the velocity within the interval is
The velocity is
Conclusion:Thus, the maximum speed of an alpha particle is from 0 to .
The frequency for maximum speed of an alpha particle within the nucleus is calculated from the formula,
Applying vx and
Conclusion:The frequency for a maximum speed of an alpha particle within the nucleus is
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