Question

Question 1 The Radial Equation for an electron in hydrogen atom can be given by [Notes, Equation SR10] (n +D! j! (21 + 1 +j)(n-1-1-j)! (an 台 Where N is the normalisation constant and the constant a' is the Bohr radius. Using the above equation and the Normalisation Condition for Radial Functions Show that 312 Where ao is the Bohr radius. The following integral identity will be useful r exp

Answer 1

"Given R_n L(r) = N/r(2 r/a n)^L + 1 exp (- r/a n) Sigma_j = 0^n - L - 1 (n + 20 !/(2 L + 1 + j)!(n - L - j)! (2 r/a n)^j putting n = 3 L = 1 Therefore R_31 (r) = N/r(2 r/3 a)^2 exp(2 r/ 3 a)^2 Sigma_j = 0^1 (-1)^j/j! 4!/(3 + j)!(1 - j)! (2 r/3 a)^j + N/r(2 r/3 a)^2 exp(-r/3 a)[1/1 4!/3! 1! + (-1)/1. 4!/4! 0! (2 r/3 a)] = N/r (2 r/3 a)^2 exp(- r/ 3 a)[4 - 2 r /3 a] Cow we have to normalize to wave function Therefore integral_0^infinity

The function is given in terms of 'a' which itself is Bohr radius as mentioned, so I did not use 'a0' there.