JEE Main · 2026 · 22 Jan 2026 · Shift 1 · Atomic Structure

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

Answer: (B)

Solution

The energy separation between two Bohr orbits of hydrogen is

Δ E = R_{H} (\frac{1}{n _{1}^{2}} - \frac{1}{n _{2}^{2}})

per atom. Converting the Rydberg constant,

R_{H} = 2.18 \times 1 0^{- 11} erg = 2.18 \times 1 0^{- 18} J

. For the jump from

n_{1} = 1

n_{2} = 2

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

. Multiplying by the Avogadro constant,

Δ E = 1.635 \times 1 0^{- 18} \times 6.022 \times 1 0^{23} = 9.835 \times 1 0^{5} J mo l^{- 1}

JEE Main · 2026 · 22 Jan 2026 · Shift 1 · Single correct option