The ratio for the speed of the electron in the $3^{\text{rd}}$ orbit of $\mathrm{He}^{+}$ to the speed of the electron in the $3^{\text{rd}}$ orbit of hydrogen atom will be:

JEE Main · 2022 · 25 Jun 2022 · Shift 1 · Modern Physics

The ratio for the speed of the electron in the

3^{rd}

orbit of

He^{+}

to the speed of the electron in the

3^{rd}

orbit of hydrogen atom will be:

(A) $1 : 1$
(B) $1 : 2$
(C) $4 : 1$
(D) $2 : 1$ ✓ Correct

Answer: (D)

Solution

From Bohr's model, the speed of an electron in the

n^{th}

orbit is proportional to

\frac{Z}{n}

, where

Z

is the atomic number.

For the same orbit (

n = 3

for both),

v \propto Z

.

For

He^{+}

Z = 2

. For hydrogen:

Z = 1

.

Therefore,

\frac{v _{He^{+}}}{v _{H}} = \frac{2}{1} = 2 : 1

JEE Main · 2022 · 25 Jun 2022 · Shift 1 · Single correct option

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