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Q.45b.

Expert-verified
Found in: Page 1237

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

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

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

The energy of the alpha particle is .

See the 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 .