The hydrogen-like species $\mathrm{Li}^{2+}$ is in a spherically symmetric state $\mathrm{S}_{1}$ with one radial node. Upon absorbing light the ion undergoes transition to a state $\mathrm{S}_{2}$. The state $\mathrm{S}_{2}$ has one radial node and its energy is equal to the ground state energy of the hydrogen atom. The orbital angular momentum quantum number of the state $\mathrm{S}_{2}$ is

JEE Advanced · 2010 · 11 Apr 2010 · Paper 2 · Atomic Structure

The hydrogen-like species

Li^{2 +}

is in a spherically symmetric state

S_{1}

with one radial node. Upon absorbing light the ion undergoes transition to a state

S_{2}

. The state

S_{2}

has one radial node and its energy is equal to the ground state energy of the hydrogen atom.

The orbital angular momentum quantum number of the state

S_{2}

(A)0
(B)1✓ Correct
(C)2
(D)3

Answer: (B)

Solution

State S₂ has energy equal to hydrogen ground state: E₂ = -13.6 eV. For Li²⁺: -13.6 × 9/n² = -13.6, so n² = 9, n = 3. S₂ has one radial node: n - l - 1 = 1, so 3 - l - 1 = 1, giving l = 1. The orbital angular momentum quantum number is 1 (p orbital).

JEE Advanced · 2010 · 11 Apr 2010 · Paper 2 · Single correct option

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