Concept explainers
The expression for the allowed energies of particle and the ground state energy for an electron.
Answer to Problem 8P
The expression for the allowed energies of particle is
Explanation of Solution
Write the expression for momentum given by de Broglie relation.
Here,
Here,
Write the expression for energy given by de Broglie relation.
Here,
Assume that particle is a wave and it must vanish at boundaries of the box so the expression for wavelength is:
Write the expression for length of particle box in terms of wavelength.
From equation (III) and equation (IV), it can be concluded that:
Similarly,
Take the square of momentum in equation (I).
Substitute
Substitute
Substitute
Conclusion:
When the electron is in the lowest energy state is
Substitute
Thus, the expression for the allowed energies of particle is
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Chapter 8 Solutions
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