Question

Write down expectation value of r for hydrogen atom.

Answer 1

Expectation value of r for hydrogen atom:

$$\big<r\big>=\int^\infty_0\psi_{1s}(r)r\psi_{1s}(r)4\pi r^2 \text{d}r=\frac{3}{2}$$

Or

$$\big<r\big>=\frac32 a_0.$$