Physical Chemistry

2nd Edition
Ball + 3 others
Publisher: Wadsworth Cengage Learning,
ISBN: 9781133958437

Physical Chemistry

2nd Edition
Ball + 3 others
Publisher: Wadsworth Cengage Learning,
ISBN: 9781133958437


Chapter 9, Problem 9.59E
Textbook Problem

Determine under what conditions of temperature and wavelength the Rayleigh-Jeans law approximates Planck’s law.

Expert Solution
Interpretation Introduction


The conditions of temperature and wavelength at which the Rayleigh-Jeans law approximates Planck’s law are to be calculated.

Concept introduction:

Planck’s equation can also be represented in the form of energy density distribution of a black body radiation at a given temperature and wavelength. This equation is known as Planck’s radiation distribution law.

Rayleigh-Jeans law gives the relation between infinitesimal amount of energy per unit volume and wavelength interval for a blackbody radiation. The relation is shown below.


Explanation of Solution

The Planck’s law is given by,


The Taylor series for the exponential term is,


In this case, the value of x=hcλkT

Apply first order approximation to the Taylor series of exponential for the Planck’s law as shown below.


Substitute the value of exponential given in equation (2) in the equation (1)

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Chapter 9 Solutions

Physical Chemistry
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