Concept explainers
(a)
Interpretation:
The wavenumber of the radiation corresponding to photons,
Concept Introduction:
A harmonic oscillator consists of a particle of mass
(a)
Answer to Problem 7E.5P
The wavenumber of the radiation corresponding to photons,
Explanation of Solution
The energy of the photons is given by the relation given below.
Where,
The value of
Where,
The energy of photons is also given by the relation below.
Where,
Substitute the equations (3) and (2) in (1).
The relation wavelength
Substitute equation (5) in (4).
Therefore, the wavenumber of the radiation corresponding to photons,
(b)
Interpretation:
The
Concept Introduction:
Refer part (a).
(b)
Answer to Problem 7E.5P
The
Explanation of Solution
The formula to calculate
Where,
The speed of light (
The vibrational frequency (
Substitute the value of
Therefore, the
(c)
Interpretation:
An expression for the force constant,
Concept introduction:
Refer part (a).
(c)
Answer to Problem 7E.5P
The expression for the force constant,
Explanation of Solution
The formula to calculate
Where,
The force constant,
Where,
Substitute the equation (7) in equation (6).
(d)
Interpretation:
The force constant and the wavenumber corresponding to the transition
Concept introduction:
Refer part (a).
(d)
Answer to Problem 7E.5P
The force constant of the
Explanation of Solution
The formula to calculate the wavenumber of the transition from
Where,
The reduced mass of
The mass of
The mass of
Substitute the value of
The conversion of
Therefore, the conversion of
The value of
The conversion of
Therefore, the conversion of
The speed of light (
Substitute the value of
The force constant of
Therefore, the force constant of the
The reduced mass of
The mass of
The mass of
Substitute the value of
The conversion of
Therefore, the conversion of
The force constant (
Substitute the value of
Therefore, the wavenumber at which the transition takes place from transition from
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