Speed of an electron in Bohr's $7^{\text {th }}$ orbit for Hydrogen atom is $3.6 \times 10^{6} \mathrm{~m} / \mathrm{s}$. The corresponding speed of the electron in $3^{\text {rd }}$ orbit, in $\mathrm{m} / \mathrm{s}$ is :

JEE Main · 2023 · 30 Jan 2023 · Shift 1 · Modern Physics

Speed of an electron in Bohr's

7^{th}

orbit for Hydrogen atom is

3.6 \times 1 0^{6} m / s

. The corresponding speed of the electron in

3^{rd}

orbit, in

m / s

is :

(A) $(1.8 \times 1 0^{6})$
(B) $(7.5 \times 1 0^{6})$
(C) $(3.6 \times 1 0^{6})$
(D) $(8.4 \times 1 0^{6})$ ✓ Correct

Answer: (D)

Solution

In the Bohr model the orbital speed falls inversely with the orbit number,

v_{n} \propto \frac{1}{n}

, so

\frac{v _{3}}{v _{7}} = \frac{7}{3}

. With

v_{7} = 3.6 \times 1 0^{6} m/s

v_{3} = \frac{7}{3} \times 3.6 \times 1 0^{6}

. The electron in the third orbit moves at

8.4 \times 1 0^{6} m/s

JEE Main · 2023 · 30 Jan 2023 · Shift 1 · Single correct option

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