JEE Main 2026 Jan 23 Shift 1, Chemistry Q1: Bohr's Atomic Model

JEE Main2026Jan 23, Shift 1Chemistry

Which of the following statements regarding the energy of the stationary state is true in the following one-electron system?

A
$- 1.09 \times 1 0^{- 18}$ J for second orbit of H atom.
B
$+ 2.18 \times 1 0^{- 18}$ J for second orbit of He $^{+}$ ion
C
$+ 8.72 \times 1 0^{- 18}$ J for first orbit of He $^{+}$ ion
D
$- 2.18 \times 1 0^{- 18}$ J for third orbit of Li $^{2 +}$ ion

Solution

For a hydrogen-like (one-electron) species: $E_{n} = - 2.18 \times 1 0^{- 18} \frac{Z ^{2}}{n ^{2}}$ J/atom. Bound-state energies are negative, so options (2) and (3) are ruled out by sign alone.

Check option (1): H ( $Z = 1$ ), $n = 2$ : $E = - 2.18 \times 1 0^{- 18} \cdot \frac{1}{4} = - 5.45 \times 1 0^{- 19}$ J. Doesn't match $- 1.09 \times 1 0^{- 18}$ J.

Check option (4): Li $^{2 +}$ ( $Z = 3$ ), $n = 3$ : $E = - 2.18 \times 1 0^{- 18} \cdot \frac{9}{9} = - 2.18 \times 1 0^{- 18}$ J. ✓

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JEE Main 2026 Jan 23 Shift 1, Chemistry Q1: Bohr's Atomic Model

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