JEE Main 2026 Jan 22 Shift 1, Chemistry Q4: Bohr's Atomic Model

JEE Main2026Jan 22, Shift 1Chemistry

The energy required by electrons, present in the first Bohr orbit of hydrogen atom to be excited to second Bohr orbit is ________ J mol $^{- 1}$ .

Given : $R_{H} = 2.18 \times 1 0^{- 11}$ ergs.

Solution

Use $Δ E = R_{H} Z^{2} (\frac{1}{n _{1}^{2}} - \frac{1}{n _{2}^{2}})$ with $Z = 1$ for hydrogen.

Convert $R_{H}$ from ergs to joules: $1 erg = 1 0^{- 7} J$ , so $R_{H} = 2.18 \times 1 0^{- 11} \times 1 0^{- 7} = 2.18 \times 1 0^{- 18}$ J.

$Δ E = 2.18 \times 1 0^{- 18} (1 - \frac{1}{4}) = 2.18 \times 1 0^{- 18} \times \frac{3}{4} = 1.635 \times 1 0^{- 18}$ J per atom.

Per mole: $1.635 \times 1 0^{- 18} \times 6.022 \times 1 0^{23} = 9.835 \times 1 0^{5}$ J mol $^{- 1}$ .

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