For a hydrogen-like ion of nuclear charge Z, write σ = Zr/a₀, where r is the distance from the…

For a hydrogen-like ion of nuclear charge $Z$, write $\sigma = \dfrac{Zr}{a_0}$, where $r$ is the distance from the nucleus and $a_0 = 52.9\ \text{pm}$. The radial parts of the wave functions of two orbitals are

A radial node is a sphere on which $\psi$ is zero (not counting $r = 0$). Consider these orbitals in the $\text{Li}^{2+}$ ion ($Z = 3$).

1. How many radial nodes does the $3s$ orbital have?
2. At what distance from the nucleus is the inner radial node of the $3s$ orbital?
3. At what distance is its outer radial node?
4. At what distance is the radial node of the $3p$ orbital?
5. How many nodes, radial and angular together, does a $3p$ orbital have?