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Q. 27

Expert-verified
Found in: Page 1176

### 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 diameter water droplet is moving with a speed of in a long box. a. Estimate the particle’s quantum number. b. Use the correspondence principle to determine whether quantum mechanics is needed to understand the particle’s motion or if it is “safe” to use classical physics.

a. the quantum number is

b. since it is too large we can use the classical approach.

See the step by step solution

## Part (a) Step 1: Given information

We have given,

Diameter of the drop =

speed of the drop =

length of he box =

we have to find the quantum number n?

## Step 2: Simplify

We know the energy of one dimensional box is

## Part (b) Step 1: Given information

We have to find its classical approach using corresponds principle.

## Step 2: Simplify

According to the correspondence principle that if any system in quantum mechanics describing the behavior of quantum systems and it must yield the same type of results as classical physics in the macroscopic limit.

then we can approach as same.

From the above found the quantum number is too large.

we can very safely use classical mechanics.