InterviewSolution
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InterviewSolution
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Radial wave function for an electron in hydrogen atom is `Psi = (1)/(16 sqrtpi) ((1)/(a_(0))^(3//2)) [(x -1) (x^(2) - 8x + 12)] e^(-x//2)` where `x = 2r//a_(0), a_(0) =` radius of first Bohr orbit. Calculate the minimum and maximum positions of radial nodes in terms of `a_(0)` |
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Answer» `Psi = (1)/(16 sqrtpi) ((1)/(a_(0))^(3//2)) [(x -1) (x^(2) -8x - 12)] e^(-x//2)` At radial node, `Psi = 0`. Hence, `(x -1) = 0 or (x^(2) -8x - 12) = 0` If `x -1 = 0`, then `x = 1`, i.e., `(2r)/(a_(0)) = 1 or r = (a_(0))/(2)` If `x^(2) -8x + 12 = 0`, i.e.,` (x -6) (x -2) = 0`, then `(x -6) = 0 or (x -2) = 0` If `(x -2) = 0`, then `x = 2 or (2r)/(a_(0)) = 2 or r = a_(0)` If `(x - 6) = 0`, then x = 6 or `(2r)/(a_(0)) = 6 or r = 3 a_(0)` Thus, nodes exist at `(a_(0))/(2), a_(0) and 3a_(0)`. Minimum is at `(a_(0))/(2)` and maximum at `3a_(0)` |
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