(a)
The expected value of
(a)
Answer to Problem 51E
The expected value of
Explanation of Solution
Write the expression for the expectation value of any physical observable
Here,
Write the expression for the wave function of the 1s electron in hydrogen atom.
Here,
Conclusion:
Substitute
Simplify the above equation.
Use the following identity to evaluate the above equation.
Rearrange the equation for the expectation value of
Thus, the expectation value of
(b)
The expectation value of
(b)
Answer to Problem 51E
The expectation value of
Explanation of Solution
Write the expression for the expectation value of any physical observable
Here,
Write the expression for the wave function of the 1s electron in hydrogen atom.
Here,
Conclusion:
Substitute
Simplify the above equation.
Use the following identity to evaluate the above equation.
Rearrange the equation for the expectation value of
Thus, the expectation value of
(c)
The reason why
(c)
Answer to Problem 51E
Both the values of the quantities are not same.
Explanation of Solution
Physically
Physically both the quantities have two different interpretations.
Conclusion:
Thus, both the values of the quantities are not same.
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Chapter 28 Solutions
General Physics, 2nd Edition
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- An excited hydrogen atom could, in principle, have aradius of 1.00 cm. What would be the value of n for a Bohrorbit of this size? What would its energy be?arrow_forwardWhat is the probability of the electron in the 1s state of the hydrogen atom being at a radius greater than the Bohr radius a0?arrow_forwardThe longest wavelength line of the Balmer Series for hydrogen occurs at 656.3 nm corresponding to the transition from n2 = 3 to n1 = 2. Determine the value for the Rydberg constant for hydrogen using these values.arrow_forward
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