The radius of the $2^{\text {nd }}$ orbit of $\mathrm{Li}^{2+}$ is x. The expected radius of the $3^{\text {rd }}$ orbit of $\mathrm{Be}^{3+}$ is

JEE Main · 2023 · 25 Jan 2023 · Shift 1 · Atomic Structure

The radius of the

2^{nd}

orbit of

Li^{2 +}

is x. The expected radius of the

3^{rd}

orbit of

Be^{3 +}

Answer: (C)

For a one-electron species the orbit radius varies as

n^{2} / Z

. The second orbit of the lithium dication, with

Z = 3

, has radius proportional to

4/3

, and this is

x

. The third orbit of the beryllium trication, with

Z = 4

, has radius proportional to

9/4

. Dividing, the required radius is

\frac{9/4}{4/3} x = \frac{27}{16} x

JEE Main · 2023 · 25 Jan 2023 · Shift 1 · Single correct option