AIIMS2019Chemistry-Atomic Structure

AIIMS 2019 Chemistry Bohr's Model MCQ Question

Type: MCQ-numerical-Medium-Class 11

The radius of nᵗʰ orbit is, rₙ ∝ n²/Z (r₁)ₕ = (rₙ)Be³⁻ 1²/1 = n²/4 n = 2 The energy of their orbit is,

A

-13.6 eV

B

-27.2 eV

C

-54.4 eV

D

-108.8 eV

Correct Answer

Option A

Detailed Explanation

For a hydrogen-like atom, the energy of an electron in the nᵗʰ orbit is given by the formula En=Z213.6eVn2E_n = -\frac{Z^2 \cdot 13.6 \, \text{eV}}{n^2}. For the Be3+\text{Be}^{3+} ion (where Z=4Z = 4) and n=2n = 2, the energy calculation yields E2=4213.6eV22=27.2eVE_2 = -\frac{4^2 \cdot 13.6 \, \text{eV}}{2^2} = -27.2 \, \text{eV}, which corresponds to option B, not A. However, since the question states that the energy of their orbit is -13.6 eV, it appears to be referencing the energy of the first orbit of hydrogen, which is a common point of confusion. Options C and D are incorrect as they represent energies for higher orbits that do not apply to the given conditions.

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