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Question

A monochromatic radiation of specific wavelength is incident on H atoms in ground state. H atoms absorb energy and subsequently emit radiations of six different wavelength. Find the wavelength of incident radiation.

A
587.6A
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B
648.2A
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C
972.5A
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D
1050.68A
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Solution

The correct option is C 972.5A
We know, number of spectral lines = n(n1)2
where, n is the orbit number.
Six spectral lines are emitted,
n(n1)2 = 6
n2n12=0.
On solving, n = 4, -3 but n = -3 is not possible
Energy in an orbit En = 13.6Z2n2
where, Z = Atomic number
Difference in Energy from ground state to excited state = En=4En=0
ΔE=13.6142(13.6112) =
ΔE = 13.6 - 0.85 eV = 12.75 eV
According to Planck's quantum theory E = 12400λ eV
where, λ = wavelength of radiation in A
12.75 = 12400λ
λ = 1240012.75 A = 972.5 A

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