The radius of the second Bohr orbit, in terms of the Bohr radius, $\mathrm{a}_{0}$, in $\mathrm{Li}^{2+}$ is

(B) $\frac{2 \mathrm{a}_{0}}{9}$

(C) $\frac{2 \mathrm{a}_{0}}{3}$

JEE Main · 2020 · 08 Jan 2020 · Shift 2 · Atomic Structure

The radius of the second Bohr orbit, in terms of the Bohr radius,

a_{0}

, in

Li^{2 +}

Answer: (A)

The radius of the

n

th Bohr orbit scales as

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

. For

Li X^{2 +}

the nuclear charge is

Z = 3

, and the second orbit has

n = 2

, so

r_{2} = a_{0} \frac{2 ^{2}}{3} = \frac{4 a _{0}}{3}

JEE Main · 2020 · 08 Jan 2020 · Shift 2 · Single correct option