Q.46 - Excercises And Problems

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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

# A small speck of dust with mass has fallen into the hole shown in FIGURE P39.46 and appears to be at rest. According to the uncertainty principle, could this particle have enough energy to get out of the hole? If not, what is the deepest hole of this width from which it would have a good chance to escape?

The value of less than the value of , so the particle will have enough energy to get out the hole. The deepest hole is for which, particle have a good chance to escape from the hole..

See the step by step solution

## Step 1: Given Information

Dust mass

Width of the box

The uncertainity principle is given by,

Where, is measurement of position, is measurement of the momentum of the particle and is plank's constant.

## Step 2:Solution

The energy and momenturm relation of particle is egven by

AlH is uncertainity in measurem ent of energy of particle.

Applying values,

The height of potertial barrier is ven by,

Where v is height af potental barrier, th is mass of particle, ts acceleratien due to graify

Apply ing values,

Hence, the oarticle all not have enough energy to get out the hole

To find the masimum height, ursig the formula.

EI

Apphing values,

Concluiton: The value of less than the value of so the particle aill have enough energy to get eut the hole. The deepest hole is "a for which, particle have a good chance to escape from the hole.