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Physics For Scientists & Engineers
Found in: Page 1296

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Short Answer

a. Calculate and graph the hydrogen radial wave function R2p(r) over the interval 0r8aBA.

b. Determine the value of r (in terms of aB ) for which R2p(r) is a maximum.

c. Example 41.3 and Figure 41.7 showed that the radial probability density for the 2p state is a maximum at r=4aB. Explain why this differs from your answer to part b.

The expression determined is R2p(r)=124πaB3r2aBe-r2aB and At r=2aB, the R2p(r) is maximum

See the step by step solution

Step by Step Solution

Part (a)

We are given R2p(r)=124πaB3r2aBe-re2aB

Then we have the following plot

Part (b)

We are given


R2p(r) is maximum when ddr(R2p(r))=0



At r=2aB, the R2p(r) is maximum

Part (c)

Probability density depends on the total wave function therefore we will not get the maximum value of the probability density at the same point where we get the maximum radial wave function.

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