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From Eq. 13.60 the normalized radial part of the hydrogenic wave function is (n - L...
The hydrogenic radial function R(r) are relatively simple for
the case l = n-1 (the maximum allowed value for l for given n):
R(r) = Arn-1 er/ab
(l = n -1)
(a) Write down the radial schrodinger equation for this
case.
(b) Verify that the proposed solution does indeed satisfy this
equation if and only if En = -Er/n2
(c) Plot the radial function R(r) for n = 0,1,2, (assume
ab=1)
3.27 Average distance from the nucleus and atomic radius The maximum in the radial probability distribution of an electron in a hydrogen-like atom is given by Equation 3.58, that is, rmax - (n'ao)/Z, for l - n- 1. The average distance F of an electron from the nucleus can be calculated by using the definition of an average and the probability distribution function Pn/(r), that is, Z. elective 2 2n2 in which the right-hand side represents the result of the...