(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
EBK MODERN PHYSICS
- Consider the HCl molecule, which consists of a hydrogen atom of mass 1 u bound to a chlorine atom of mass 35 u. The equilibrium separation between the atoms is 0.128 nm, and it requires 0.15 eV of work to increase or decrease this separation by 0.01 nm. (a) Calculate the four lowest rotational energies (in eV) that are possible, assuming the molecule rotates rigidly. (b) Find the molecules spring constant and its classical frequency of vibration. (Hint: Recall that U=12Kx2.) (c) Find the two lowest vibrational energies and the classical amplitude of oscillation corresponding to each of these energies. (d) Determine the longest wavelength radiation that the molecule can emit in a pure rotational transition and in a pure vibrational transition.arrow_forwardCompare the effective force constant for the CO molecule deduced here with that of an ordinary laboratory spring that stretches 0.5 m when a 1.0 kg mass is suspended from it.arrow_forwardConsider a CO molecule that is initially in the ground state of n = 0, l = 0. If the energy of a vibrational transition from the n = 0 state to the n = 1 state in CO could instead be absorbed in a rotational transition, what would be the value of l for the final state?arrow_forward
- Modern PhysicsPhysicsISBN:9781111794378Author:Raymond A. Serway, Clement J. Moses, Curt A. MoyerPublisher:Cengage LearningPhysics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning