Explanation The natural population of atoms in thermal equilibrium at any temperature ( T ) is expressed as follows, N N 0 = e − Δ E k T Here, N is the number of atoms in energy level E , N 0 is the number of atoms in energy level E 0 , k is the Boltzman’s constant whose value is 1.38 × 10 − 23 J / K and T is the required temperature of the system. The energy levels of chromium in a ruby crystal is given in figure 1. Figure 1 Given data: The number of atoms in the energy level E 2 would have half as many atoms as in energy level E 0 , therefore, N 2 N 0 = 1 2 Here, N 2 is the number of atoms in energy level E 2 . From figure 1, the energy level difference between the energy levels E 2 and E 0 is expressed as, Δ E 20 = E 2 − E 0 (I) The fraction of atoms for energy level E 2 relative to E 0 is given by, N 2 N 0 = e − Δ E 20 k T Rearrange the above equation to find T . e − Δ E 20 k T = N 2 N 0 e Δ E 20 k T = N 0 N 2 Δ E 20 k T = ln ( N 0 N 2 ) T = Δ E 20 k ln ( N 0 N 2 ) (II) Conclusion: Substitute 2

Physics for Scientists and Engineers with Modern Physics

4th Edition

ISBN: 9780131495081

Author: Douglas C. Giancoli

Publisher: Addison-Wesley

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Chapter 39, Problem 59P

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The required temperature of the system.

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Chapter 39, Problem 58P

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Chapter 39 Solutions

Physics for Scientists and Engineers with Modern Physics

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The required temperature of the system.

Solution Summary: The author analyzes the energy levels of chromium in a ruby crystal.

The required temperature of the system.

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Chapter 39 Solutions