Concept explainers
The expression for average particle position; evaluate the results for mean position; the amplitude of oscillation for an electron in a well; the time to shuttle back and forth in a well; the same time classically for an electron.
Answer to Problem 38P
Average position of particle is
Explanation of Solution
Write the expression for average position.
Substitute
Write the expression for mean position.
Write the expression for amplitude of oscillation.
Write the expression for energy of particle.
Write the expression for time required.
Write the expression for velocity in terms of kinetic energy.
Write the expression for classical time required.
Conclusion:
For last two integrals, the integral value of both is same as the functions
Substitute
Thus, average position of particle is
The average position of particle for any stationary state of well is
Substitute
Thus, the mean position value is
Thus, the amplitude value is
Substitute
Substitute
Substitute 1.51 eV for
Thus, time required is equal to
Calculate the kinetic energy of electron.
Substitute
Substitute 1 nm for
Thus, classical time required is equal to
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