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Q.45b.

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
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Short Answer

What energy (in MeV) alpha particle has a de Broglie wavelength equal to the diameter of nucleus?

The energy of the alpha particle is .

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Step by Step Solution

Step.1

Nuclear radius depends on mass number of nucleus as follows.

Here, is a constant and is mass number.

Substitute 1.2 fm for and 238 for , calculated the radius of nucleus.

Convert the unit for nuclear radius from fm to .

Diameter of the nucleus is,

From the given data, the de Broglie wavelength of the particle is equal to the diameter of the nucleus.

Step.2

The de Broglie wavelength of alpha particle is,

Here, is Plank's constant and is momentum.

Rewrite this equation for momentum,

A moving particle has only kinetic energy, the relation between momentum and energy of the particle is,

Substitute for ,

Step.3

Convert atomic mass of the particle from u to .

Substitute for for and for in the

equation .

Convert the units for energy from to .

Therefore, the energy of the alpha particle is .

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