An unnormalized wave function of the hydrogen atom is given by r² er / 3 (3 cos ² θ-1). The three quantum… · ABC26PH1315
Subject: Physical Chemistry · Chapter: Quantum Chemistry · Topic: Hydrogen Atom · Exam: CSIR NET JUNE 2016 · Marks: 2 · Difficulty: Medium
An unnormalized wave function of the hydrogen atom is given by $\mathrm{r}^{2} \mathrm{e}^{\mathrm{r} / 3}\left(3 \cos ^{2} \theta-1\right)$. The three quantum numbers, n, 1and m, associated with this orbital are, respectively.
(a)2, 2, 0
(b)2, 1, 1
(c)3, 2, 0
(d)3, 1, 1
Answer
Answer: C ✓ checked by 4AB · confidence high
The source book printed no answer; this one was worked out and checked — see the explanation.
Explanation
r²e^{−r/3} with no radial node ⇒ l = 2, n = 3; (3cos²θ − 1) is Y₂₀ ⇒ m = 0: (3, 2, 0), the 3d_z² orbital.