Concept explainers
(a)
Interpretation:
The transition of an electron form ground state
Concept introduction:
A term symbol describes the orbital, spin and total angular momenta of an electronic state. The symbol
(a)

Answer to Problem 8.1IA
The transition of an electron from ground state
Explanation of Solution
The term symbol for the
Where,
The value of
The value of
Therefore the value of
The value of
Therefore, the value of
As the orbital is less than half filled in excited state
Substitute the value of
Substitute the value of
Therefore the term symbol for the excited state of
The ground state configuration of
The value of
The value of
Therefore the value of
The value of
Therefore, the value of
The total angular momentum
Substitute the value of
Substitute the value of
Therefore the term symbol for the excited state of
Therefore, the transition occurs from
(b)
Interpretation:
The wavelength, frequency and wavenumber of the transition has to be calculated.
Concept introduction:
The wavelength, frequency and wavenumber of transition are all related to the energy of the transition. The wavelength is inversely proportional to the energy of transition. The frequency and wavenumber are directly proportional to energy of transition.
(b)

Answer to Problem 8.1IA
The frequency of the transition is
Explanation of Solution
The energy of transition of the hydrogen like atom is given below.
Where,
The atomic number of
The transition takes place from
Substitute the value of
The formula to calculate frequency
Where,
The value of Planck’s constant (
Substitute the value of
Therefore, frequency of the transition is
The wavelength (
Where,
The speed of light is
Substitute the value of
Therefore, wavelength of the transition is
The relation wavelength
Substitute the value of
Therefore, the wavenumber is
(c)
Interpretation:
The change in mean radius of electron during the transition has to be calculated.
Concept introduction:
The total distance from the nucleus of an atom to its outermost shell, where probability of finding the electron is maximum is termed as radius of the atom. The most probable distance of the electron form nucleus in the ground state of hydrogen atom is termed as Bohr’s radius.
(c)

Answer to Problem 8.1IA
The change in mean radius during transition is
Explanation of Solution
The mean radius of the electron is given by the formula shown below.
Where,
The atomic number of
Substitute the value of
The ground state configuration of
The value of
The value of
Substitute the value of
Therefore, the change in radius during transition is calculated below.
Therefore, the change in mean radius during transition is
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Chapter 8 Solutions
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