Chapter 30, Problem 32PE

### College Physics

1st Edition
Paul Peter Urone + 1 other
ISBN: 9781938168000

Chapter
Section

### College Physics

1st Edition
Paul Peter Urone + 1 other
ISBN: 9781938168000
Textbook Problem

# Ruby lasers have chromium atoms doped in an aluminum oxide crystal. The energy level diagram for chromium in a ruby is shown in Figure 30.64. What wavelength is emitted by a ruby laser?Figure 30.64 Chromium atoms in an aluminum oxide crystal have these energy levels, one of which is metastable. This is the basis of a ruby laser. Visible light can pump the atom into an excited state above the metastable state to achieve a population inversion.

To determine

The wavelength emitted by ruby laser when Ruby lasers have chromium atoms doped in an aluminum oxide crystal.

Explanation

Given Data:

Given energy-level diagram for chromium in a ruby.

â€ƒâ€ƒ

Formula Used:

Energy is given as

â€ƒâ€ƒE=hcÎ»

Where, E= Energy

â€ƒâ€ƒh= Planck's constant

â€ƒâ€ƒc= Speed of light

â€ƒâ€ƒÎ»= Wavelength

Energy released during transition between metastable state and ground state is given as

â€ƒâ€ƒÎ”E=Emâˆ’Eg

Where Î”E= Energy released during the transition between two states

â€ƒâ€ƒEm= Energy of meta- stable state

â€ƒâ€ƒEg= Energy of ground state

Calculation:

From energy level diagram,

â€ƒâ€ƒEm=1.79â€‰eV

â€ƒâ€ƒEg=0â€‰eV

Energy released during transition is calculated as

â€ƒâ€ƒÎ”E=(1.79eV)âˆ’(0eV)

â€ƒâ€ƒÎ”E=1.79eV

Now, wavelength emitted by ruby laser is calculated using Planck's equation

We have h=6.626Ã—10âˆ’34J.s

â€ƒâ€ƒE=1.79eV

â€ƒâ€ƒc=3Ã—108m/sec

Substituting the values in equation of energy, we have

â€ƒâ€ƒE=hcÎ»

â€ƒâ€ƒ1

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