Question

( 25 marks) The normalized wave function for a hydrogen atom in the \(2 s\) state is

$$ \psi_{2 s}(r)=\frac{1}{\sqrt{32 \pi a^{3}}}\left(2-\frac{r}{a}\right) e^{-r / 2 a} $$

where \(a\) is the Bohr radius. (a) In the Bohr model, the distance between the electron and the nucleus in the \(n=2\) state is exactly \(4 a\). Calculate the probability that an electron in the \(2 s\) state will be found at a distance less than \(4 a\) from the nucleus. (b) At what value of \(r\) is the radial distribution probability \(P(r) d r\) equal to zero, so that the probability of finding the electron at that separation from the nucleus is zero? There can be more than one such separation.

Answer 1