JEE Main · 2025 · 02 Apr 2025 · Shift 2 · Modern Physics

Assuming the validity of Bohr's atomic model for hydrogen like ions the radius of

L i^{++}

ion in its ground state is given by

\frac{1}{X} a_{0}

, where

X =

______.
(Where

a_{0}

is the first Bohr's radius.)

(A)2
(B)1
(C)3✓ Correct
(D)9

Answer: (C)

Solution

According to Bohr's model, the radius of the

n

-th orbit for a hydrogen-like ion is

r = a_{0} \frac{n ^{2}}{Z}

, where

Z

is the atomic number. For

L i^{++}

(lithium with 2 electrons removed),

Z = 3

. In the ground state,

n = 1

. Therefore,

r = a_{0} \frac{1 ^{2}}{3} = \frac{a _{0}}{3}

. Hence

X = 3

JEE Main · 2025 · 02 Apr 2025 · Shift 2 · Single correct option

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