Concept explainers
(a)
The expression for orbital radii and energies.
(a)
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Answer to Problem 5.8P
The expression for orbital radii is
Explanation of Solution
Write the expression for force between two charges.
Here,
Write the expression for electric potential energy between two charges.
Write the expression for kinetic energy of the electron.
Here,
Write the expression for centripetal force between electron and the nucleus.
Write the expression for Bohr’s quantization of angular momentum.
Here,
Write the expression for total orbital energy.
Conclusion:
Substitute
The centripetal force is equal to force between two charges.
Substitute
Substitute
Substitute
Substitute
Thus, the expression for orbital radii is
(b)
The radius and energy of ground state orbit and ionization energy of the singly ionized helium.
(b)
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Answer to Problem 5.8P
The radius of ground state orbit is
Explanation of Solution
Write the expression for radius of ground state orbit.
Write the expression for energy of ground state orbit.
Conclusion:
Substitute
Substitute
Thus, the radius of ground state orbit is
(c)
The radius and energy of ground state orbit or ionization energy of the doubly ionized lithium.
(c)
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Answer to Problem 5.8P
The radius of ground state orbit is
Explanation of Solution
The equation
Conclusion:
Substitute
Substitute
Thus, the radius of ground state orbit is
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Chapter 5 Solutions
EBK AN INTRODUCTION TO MODERN ASTROPHYS
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