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Chapter 40: Q. 27 (page 1176)

A 2.0渭尘diameter water droplet is moving with a speed of 1.0mm/sin a 20渭尘long box.

a. Estimate the particle鈥檚 quantum number.

b. Use the correspondence principle to determine whether quantum mechanics is needed to understand the particle鈥檚 motion or if it is 鈥渟afe鈥� to use classical physics.

Short Answer

Expert verified

a. the quantum number is 2.52脳108.

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

Step by step solution

01

Part (a) Step 1: Given information

We have given,

Diameter of the drop =2渭尘

speed of the drop =1mm/s

length of he box =20渭尘

we have to find the quantum number n?

02

Simplify

We know the energy of one dimensional box is

E=n2h28mL2n=8mL2Eh212n=8(蚁脳43蟺谤3脳L2脳12mv2h21/2n=8脳103kg/m3脳(4蟺脳10-6m)脳400脳10-12脳103脳4蟺脳10-6m脳10-3m/s3脳2脳3脳6.63脳10-34j/sn=2.52脳108

03

Part (b) Step 1: Given information

We have to find its classical approach using corresponds principle.

04

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.

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