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Question

Hydrogen atoms in the ground state are excited by monochromatic radiation of photon energy 12.1 eV. According to Bohr's theory, the spectral lines emitted by hydrogen will be

A
two
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B
three
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C
four
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D
one
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Solution

The correct option is B three
When an electron is excited from an energy level ni to an energy level nf then the energy gap ΔE is given by
ΔE=13.6Z2(1n2i1n2f)
Energy provided is 12.1 eV and Z=1 for hydrogen. Also ni=1 for ground state electrons.
Hence
12.1=13.6(11n2f)
which gives nf=3
Now no. of emissions lines is given by
n(n1)2
Here n=3. Hence no. of spectral lines emitted
= 3×22=3

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