During the transition of electron from state A to state C of a Bohr atom, the wavelength of emitted radiation is $2000 \AA$ and it becomes $6000 \AA$ when the electron jumps from state B to state C. Then the wavelength of the radiation emitted during the transition of electrons from state A to state B is :-

JEE Main · 2025 · 24 Jan 2025 · Shift 1 · Modern Physics

During the transition of electron from state A to state C of a Bohr atom, the wavelength of emitted radiation is

2000 \overset{˚}{A}

and it becomes

6000 \overset{˚}{A}

when the electron jumps from state B to state C. Then the wavelength of the radiation emitted during the transition of electrons from state A to state B is :-

(A) $3000 \overset{˚}{A}$ ✓ Correct
(B) $6000 \overset{˚}{A}$
(C) $4000 \overset{˚}{A}$
(D) $2000 \overset{˚}{A}$

Answer: (A)

Solution

Let the energy levels be

E_{A} > E_{B} > E_{C}

. Using

E = \frac{h c}{λ}

for each transition:

E_{A} - E_{C} = \frac{h c}{2000 A ˚}

... (1)

E_{B} - E_{C} = \frac{h c}{6000 A ˚}

... (2)

The energy released in the A → B transition is

E_{A} - E_{B} = (E_{A} - E_{C}) - (E_{B} - E_{C})

\frac{h c}{λ _{A B}} = \frac{h c}{2000} - \frac{h c}{6000}

\frac{1}{λ _{A B}} = \frac{1}{2000} - \frac{1}{6000} = \frac{3 - 1}{6000} = \frac{1}{3000}

λ_{A B} = 3000

JEE Main · 2025 · 24 Jan 2025 · Shift 1 · Single correct option

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JEE Main · 2025 · 24 Jan 2025 · Shift 1 · Modern Physics

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