(a)
Show that the force on an ion in ionic solid.
(a)
Answer to Problem 6P
The force on an ion in ionic solid is proved has
Explanation of Solution
The total potential energy stored in the solid object is,
Here,
From problem (1) the value of the magnetic field is,
Here,
Conclusion:
Substitute equation (II) in equation (I).
The force on an ion in ionic solid is,
Therefore, the force on an ion in ionic solid is proved has
(b)
Show that the ion experiences a restoring force.
(b)
Answer to Problem 6P
The ion experiences a restoring force is
Explanation of Solution
From part (a),
Consider that atom is displaced by a small distance
Here,
Conclusion:
Substitute the condition
Neglect the term
Therefore, the ion experience a restoring force
(c)
The frequency of vibration of
(c)
Answer to Problem 6P
The frequency of vibration of
Explanation of Solution
From part (b),
The effective force constant is,
Write the expression for frequency of vibration.
Here,
Conclusion:
Substitute
Substitute
Therefore, the frequency of vibration of
(d)
The wavelength of the Na+ ion absorb incident
(d)
Answer to Problem 6P
The wavelength of the Na+ ion absorb incident radiation is
Explanation of Solution
Write the expression for wavelength of the radiation.
Here,
Conclusion:
Substitute
The above wavelength >> 800nm, therefore absorption is in infrared spectrum.
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Chapter 12 Solutions
Modern Physics
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- Modern PhysicsPhysicsISBN:9781111794378Author:Raymond A. Serway, Clement J. Moses, Curt A. MoyerPublisher:Cengage Learning