Concept explainers
(a)
Plot of wave function as a function of
(a)
Answer to Problem 74P
The wave function was plotted as a function of
Explanation of Solution
Write the given wave function of the electron.
Here,
Write the formula to calculate the probability of finding a particle in a certain range.
Here,
Refer equation (I) and plot the wave function as a function of
Figure 1 below shows the plot of wave function.
Conclusion:
The wave function was plotted as a function of
(b)
Plot of probability density as a function of
(b)
Answer to Problem 74P
The probability density was plotted as a function of
Explanation of Solution
Write the given wave function of the electron.
Here,
Write the formula to calculate the probability of finding a particle in a certain range.
Here,
Refer equation (II) and plot the probability density as a function of
Figure 2 below shows the plot of wave function.
Conclusion:
The probability density was plotted as a function of
(c)
To show that
(c)
Answer to Problem 74P
The
Explanation of Solution
Write the given wave function of the electron.
Here,
For the wave function to be a reasonable wave function, there are set of condition.
The
As
The
The
Conclusion:
The
(d)
To normalize the wave function.
(d)
Answer to Problem 74P
The normalization constant of the given wave function is
Explanation of Solution
Write the given wave function of the electron.
Here,
Write the condition for normalized wave function.
The wave function is symmetric. Thus re-write the above condition.
Substitute equation (I) in the above equation.
Conclusion:
The normalization constant of the given wave function is
(e)
The probability of finding the electron in the range
(e)
Answer to Problem 74P
The probability of finding the particle in the range
Explanation of Solution
Refer section (d) and write the given normalized wave function of the electron.
Here,
Write the formula to calculate the probability of finding a particle in a certain range.
Here,
Refer equation (II) in equation (III) to determine probability in range
Conclusion:
The probability of finding the particle in the range
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Chapter 28 Solutions
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