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Chapter 6: Q3E (page 1401)

A photon is emitted when an electron in a three-dimensional cubical box of side length 8.00脳10-11mmakes a transition from thenx=2,nY=2,nz=1state to thenx=1,nY=1,nz=1state. What is the wavelength of this photon?

Short Answer

Expert verified

The wavelength of the photon is 3.52nm.

Step by step solution

01

Energy of a photon of wavelength

In a cubical box with side length L, the allowed energies for a particle of mass m are given by;

The energy of a photon of wavelength is calculated as:

02

Wavelength of the photon

Given;

The cubical box's side length is

An electron's mass is

Therefore, for the upper state


Therefore, for the lower state

The energy difference between the two levels is;

on putting the equation together;

A photon is emitted when an electron transitions from an upper to a lower level.

The energy separation between the two levels is equal to the photon's energy, so:

Putting the values now;

Hence, the wavelength of the photon is 3.52nm.

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