Concept explainers
In exercise 11.57 regarding
Interpretation:
The total angular momenta of the electron of the given state that has quantum number
Concept introduction:
The total angular momentum for the 3-Dimensional system is given by,
The total angular momentum does not depend on the mass of the particle, radius of the rotation and also the magnetic quantum number.
The z-component of the three dimensional angular momentum that has components in x, y and z direction is quantized. Its value depends on the magnetic quantum number and it is given by,
Answer to Problem 11.58E
The total angular momenta of the electron of the given state that has quantum number
The z-components of the angular momentum for the state
The z-components of the angular momentum for the state
The z-components of the angular momentum for the state
The z-components of the angular momentum for the state
Explanation of Solution
The moment of inertia for the electron in the spherical
The total angular momentum for the 3-D rotational wavefunction is calculated using the formula,
Where,
•
•
•
For
Thus, the total angular momentum of the electron in spherical
For
Thus, the total angular momentum of the electron in spherical
For
Thus, the total angular momentum of the electron in spherical
For
Thus, the total angular momentum of the electron in spherical
The relation between the Z-component of angular momentum and magnetic quantum number for 3-dimensional rotation is
Where,
•
•
The possible vales of
The Z-component of angular momentum to by substituting the values of magnetic quantum number in the given formula is
The possible vales of
The Z-component of angular momentum to by substituting the values of magnetic quantum number in the given formula is
The possible vales of
The Z-component of angular momentum to by substituting the values of magnetic quantum number in the given formula is
The possible vales of
The Z-component of angular momentum to by substituting the values of magnetic quantum number in the given formula is
The total angular momenta of the electron of the given state that has quantum number
The z-components of the angular momentum for the state
The z-components of the angular momentum for the state
The z-components of the angular momentum for the state
The z-components of the angular momentum for the state
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Chapter 11 Solutions
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