JEE Main 2025 Apr 8 Shift 2, Chemistry Q22: Bohr's Atomic Model

JEE Main2025Apr 8, Shift 2Chemistry

The energy of an electron in the first Bohr orbit of H-atom is $- 13.6$ eV. The magnitude of the energy value of the electron in the first excited state of Be $^{3 +}$ is ______ eV. (nearest integer value)

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Solution

The Bohr energy for a hydrogen-like species is $E_{n} = - 13.6 \frac{Z ^{2}}{n ^{2}}$ eV.

Be $^{3 +}$ is a hydrogen-like ion with a single electron and atomic number $Z = 4$ .

The first excited state corresponds to $n = 2$ .

Substituting: $E_{2} = - 13.6 \times \frac{4 ^{2}}{2 ^{2}} = - 13.6 \times \frac{16}{4} = - 13.6 \times 4 = - 54.4$ eV.

The magnitude, rounded to the nearest integer, is 54 eV.

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JEE Main 2025 Apr 8 Shift 2, Chemistry Q22: Bohr's Atomic Model

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