JEE Main · 2023 · 11 Apr 2023 · Shift 1 · Modern Physics

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A monochromatic light is incident on a hydrogen sample in ground state. Hydrogen atoms absorb a fraction of light and subsequently emit radiation of six different wavelengths. The frequency of incident light is

x \times 1 0^{15}) Hz

. The value of x is
_____. (Given

h = 4.25 \times 1 0^{- 15} eVs

)

Answer: 3

Solution

Six distinct emission wavelengths correspond to

\frac{n ( n - 1 )}{2} = 6

, so the atoms are raised to

n = 4

. The absorbed photon carries the energy from the ground state to this level,

h ν = 13.6 (1 - \frac{1}{16}) = 13.6 \times \frac{15}{16} = 12.75

eV. Thus

ν = \frac{12.75}{4.25 \times 1 0 ^{- 15}} = 3 \times 1 0^{15}

Hz, giving

x = 3

JEE Main · 2023 · 11 Apr 2023 · Shift 1 · Integer answer

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