JEE Main 2025 Jan 24 Shift 1, Physics Q5: The Line Spectra of the Hydrogen Atom

JEE Main2025Jan 24, Shift 1Physics

During the transition of electron from state A to state C of a Bohr atom, the wavelength of emitted radiation is 2000 Å and it becomes 6000 Å 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
$3000$ Å
B
$6000$ Å
C
$4000$ Å
D
$2000$ Å

Solution

Energy levels satisfy $E_{A} > E_{B} > E_{C}$ (A is the highest of the three). The photon energy for a transition from level X to level Y is $h c / λ_{X Y} = E_{X} - E_{Y}$ .

From the data:

$E_{A} - E_{C} = \frac{h c}{2000 A ˚}, E_{B} - E_{C} = \frac{h c}{6000 A ˚}$

Subtract:

$E_{A} - E_{B} = (E_{A} - E_{C}) - (E_{B} - E_{C}) = \frac{h c}{2000} - \frac{h c}{6000} = \frac{h c}{3000 A ˚}$

Hence $λ_{A B} = 3000$ Å.

$∴$ Option (1).

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JEE Main 2025 Jan 24 Shift 1, Physics Q5: The Line Spectra of the Hydrogen Atom

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