(a)
The potential energy of the system of all pairs of interaction.
(a)
Answer to Problem 15P
Total potential energy of the system is
Explanation of Solution
Write the expression for potential energy.
Here,
Conclusion:
Substitute
Similarly, for other pairs, the potential energy is calculated.
The table of potential energy for all pairs is drawn below.
S. No. | Charge 1 | Charge 2 | Distance b/w charges | Potential Energy |
1. | ||||
2. | ||||
3. | ||||
4. | ||||
5. | ||||
6. |
The total potential of all pairs is the sum of potential energy of each pair.
Calculate the total energy.
Thus, total potential energy of the system is
(b)
The minimum kinetic energy of two electrons.
(b)
Answer to Problem 15P
Minimum kinetic energy of two electrons is
Explanation of Solution
Write the expression for kinetic energy of electron.
Here,
Conclusion:
Substitute 1 for
Kinetic energy of two electrons would be two times of the above value.
Thus, minimum kinetic energy of two electrons is
(c)
The value of
(c)
Answer to Problem 15P
The value of
Explanation of Solution
Write the expression for total energy.
Here,
Substitute
First derivative of energy should be zero for minimum total energy.
Rearrange the above expression in terms of
Conclusion:
Substitute
Thus, the value of
(d)
To compare the value of
(d)
Answer to Problem 15P
Atomic spacing is 2.8 times larger than
Explanation of Solution
Write the expression for volume.
Here,
Multiply both sides with
Rearrange the above expression in terms of
Substitute
Here,
Conclusion:
Substitute
Thus, atomic spacing is 2.8 times larger than
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Chapter 6 Solutions
Modern Physics
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