Q81 · CSIR-NET Chemistry, June 2012

Paper: CSIR-NET June 2012 · Subject: Physical Chemistry · Chapter: Quantum Chemistry · Topic: Hydrogen Atom · Marks: 2 · Difficulty: Medium

For hydrogen-like atom with a nuclear charge Z , the energy of orbital with principal quantum number 'n' follows the relation.

(a)$\mathrm{E}_{\mathrm{n}} \propto \mathrm{n}^{2} \mathrm{Z}^{2}$

(b)$\mathrm{E}_{\mathrm{n}} \propto-\frac{\mathrm{Z}^{2}}{\mathrm{n}}$

(c)$\mathrm{E}_{\mathrm{n}} \propto \frac{\mathrm{Z}}{\mathrm{n}}$

(d)$\mathrm{E}_{\mathrm{n}} \propto-\frac{\mathrm{Z}^{2}}{\mathrm{n}^{2}}$

Answer

Answer: D ✓ checked by 4AB · confidence high

The source book printed no answer; this one was worked out and checked — see the explanation.

Explanation

For a hydrogen-like ion, Eₙ = −13.6 Z²/n² eV, so Eₙ ∝ −Z²/n² (d).

Study loop for Quantum Chemistry