Concept explainers
(a)
Interpretation:
The value and units of the slope of the energy versus wavelength for given Planck’s law equation at given temperatures and wavelengths is 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.
Answer to Problem 9.30E
The value and units of the slope of the energy versus wavelength at given temperature and wavelength is
Explanation of Solution
It is given that temperature and wavelength is
To calculate slope of the energy versus wavelength, the Planck’s law equation used is,
Where,
•
•
•
•
•
Substitute the values of constants, temperature and wavelength in the given equation.
Thus, the slope of the energy versus wavelength is
The value and units of the slope of the energy versus wavelength at given temperature and wavelength is
(b)
Interpretation:
The value and units of the slope of the energy versus wavelength for given Planck’s law equation at given temperatures and wavelengths is 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.
Answer to Problem 9.30E
The value and units of the slope of the energy versus wavelength at given temperature and wavelength is
Explanation of Solution
It is given that temperature and wavelength is
To calculate slope of the energy versus wavelength, the Planck’s law equation used is,
Where,
•
•
•
•
•
Substitute the values of constants, temperature and wavelength in the given equation.
Thus, the slope of the energy versus wavelength is
The value and units of the slope of the energy versus wavelength at given temperature and wavelength is
(c)
Interpretation:
The value and units of the slope of the energy versus wavelength for given Planck’s law equation at given temperatures and wavelengths is 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.
Answer to Problem 9.30E
The value and units of the slope of the energy versus wavelength at given temperature and wavelength is
Explanation of Solution
It is given that temperature and wavelength is
To calculate slope of the energy versus wavelength, the Planck’s law equation used is,
Where,
•
•
•
•
•
Substitute the values of constants, temperature and wavelength in the given equation.
Thus, the slope of the energy versus wavelength is
The value and units of the slope of the energy versus wavelength at given temperature and wavelength is
(d)
Interpretation:
The value and units of the slope of the energy versus wavelength for given Planck’s law equation at given temperatures and wavelengths is 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.
Answer to Problem 9.30E
The value and units of the slope of the energy versus wavelength at given temperature and wavelength is
Explanation of Solution
It is given that temperature and wavelength is
To calculate slope of the energy versus wavelength, the Planck’s law equation used is,
Where,
•
•
•
•
•
Substitute the values of constants, temperature and wavelength in the given equation.
Thus, the slope of the energy versus wavelength is
The value and units of the slope of the energy versus wavelength at given temperature and wavelength is
(e)
Interpretation:
The results are to be compared with those of exercise
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.
The slope of the plot of energy versus wavelength for the Rayleigh-Jeans law is given by a rearrangement of equation
Answer to Problem 9.30E
The values of slope of the plot of energy versus wavelength from Rayleigh-Jeans law is similar to that of Planck’s radiation distribution law at temperature and wavelength
Explanation of Solution
On comparing the results from exercise
The values of slope of the plot of energy versus wavelength from Rayleigh-Jeans law is similar to that of Planck’s radiation distribution law at temperature and wavelength
(f)
Interpretation:
The temperatures and spectral regions at which the Rayleigh-Jeans law is close to Planck’s law are to be identified.
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.
The slope of the plot of energy versus wavelength for the Rayleigh-Jeans law is given by,
Answer to Problem 9.30E
At higher temperatures and longer wavelengths, the Rayleigh-Jeans law is close to Planck’s law.
Explanation of Solution
On comparing the results from exercise
At higher temperatures and longer wavelengths the Rayleigh-Jeans law is close to Planck’s law.
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Chapter 9 Solutions
Physical Chemistry
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