The quantum-mechanical treatment of the hydrogen atom gives this expression for the wave

Chapter 7, Problem 7.79

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The quantum-mechanical treatment of the hydrogen atom gives this expression for the wave function, c, of the 1s orbital: 5 1 "p a 1 a0 b 3/2 e2r/a0 where r is the distance from the nucleus and a0 is 52.92 pm. The probability of finding the electron in a tiny volume at distance r from the nucleus is proportional to c2. The total probability of finding the electron at all points at distance r from the nucleus is proportional to 4pr2 c2 . Calculate the values (to three significant figures) of c, c2, and 4pr2c2 to fill in the following table and sketch a plot of each set of values versus r. Compare the latter two plots with those in Figure 7.17A, p. 311: r(pm) (pm23/2) 2 (pm23) 4r 22 (pm21) 0 50 100 200