Show that the probability of finding the electron within1

Chapter 39, Problem 39.26

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QUESTION:

Show that the probability of finding the electron within1 Bohr radius of the nucleus in the hydrogen atom is(a) 3.4% for the n = 2, = 0 state, and (b) 0.37% for then = 2, = 1 state. (See 21.)

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QUESTION:

Show that the probability of finding the electron within1 Bohr radius of the nucleus in the hydrogen atom is(a) 3.4% for the n = 2, = 0 state, and (b) 0.37% for then = 2, = 1 state. (See 21.)

ANSWER:

Step 1 of 3

(a)

The probability density over any radii range  is,

                                                        

For easier calculation let, .

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