Question

What is the radial distribution function P(r) for a 2p_z orbital? What is the probability of finding an electron in a shell of 1.00 pm thickness at radius 50.0 pm?

Answer 1

For a 2p_z orbital, the radial distribution function P(r) is given by = P(r) = r²R_2p² .

Here, R_2p is the radial wave function for the 2p_z orbital.

We also know that, the radial wave function is = R_2p = (1/2√6) × ρ × Z^3/2 × e^-ρ/2.

Here, r = radius expressed in atomic units, Z = effective nuclear charge for that orbital in that atom and  ρ = 2Zr/n where n is the principal quantum number (2 for the 2porbitals).

Therefore, P(r)= r² * (1/2√6) × ρ × Z^3/2 × e^-ρ/2)².