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. Energy of the state $\mathrm{S}_{1}$ in units of the hydrogen atom ground state energy 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.

Energy of the state

S_{1}

in units of the hydrogen atom ground state energy is

(A)0.75
(B)1.50
(C)2.25✓ Correct
(D)4.50

Answer: (C)

Solution

For hydrogen-like species, E = -13.6 Z²/n² eV. For Li²⁺ (Z=3) in state S₁ (n=2): E₁ = -13.6 × 9/4 = -30.6 eV. The ground state energy of hydrogen is -13.6 eV. The ratio is |E₁|/|E_H| = 30.6/13.6 = 2.25.

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

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