The time period of revolution of electron in its ground state orbit in a hydrogen atom is $1.6 \times 10^{-16}\,\text{s}$. The frequency of revolution of the electron in its first excited state (in $\text{s}^{-1}$) is

JEE Main · 2020 · 07 Jan 2020 · Shift 1 · Modern Physics

The time period of revolution of electron in its ground state orbit in a hydrogen atom is

1.6 \times 1 0^{- 16} s

. The frequency of revolution of the electron in its first excited state (in

s^{- 1}

) is

(A) $7.8 \times 1 0^{14}$ ✓ Correct
(B) $1.6 \times 1 0^{14}$
(C) $6.2 \times 1 0^{15}$
(D) $5.6 \times 1 0^{12}$

Answer: (A)

Solution

In the Bohr model the period of revolution scales as

T \propto n^{3}

, so the frequency

ν = 1/ T \propto 1/ n^{3}

. Going from the ground state

n = 1

to the first excited state

n = 2

\frac{ν _{2}}{ν _{1}} = \frac{1}{2 ^{3}} = \frac{1}{8}

. With

T_{1} = 1.6 \times 1 0^{- 16} s

ν_{2} = \frac{1}{8 T _{1}} = \frac{1}{8 \times 1.6 \times 1 0 ^{- 16}} \approx 7.8 \times 1 0^{14} s^{- 1}

JEE Main · 2020 · 07 Jan 2020 · Shift 1 · Single correct option

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