Hydrogen atom in ground state is excited by a monochromatic radiation of = 975 . Number of spectral lines in the resulting spectrum emitted will be [2014]

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Solution

Q.
Hydrogen atom in ground state is excited by a monochromatic radiation of $λ$ = 975 $Å$ . Number of spectral lines in the resulting spectrum emitted will be [2014]

1 3

2 2

3 6

4 10

Ans.
(3)

Energy of the photon, $E = \frac{h c}{λ}$

$E = \frac{6.63 \times 10^{- 34} \times 3 \times 10^{8}}{975 \times 10^{- 10}} J$

$= \frac{6.63 \times 10^{- 34} \times 3 \times 10^{8}}{975 \times 10^{- 10} \times 1.6 \times 10^{- 19}} eV = 12.75$ $eV$

After absorbing a photon of energy 12.75 eV, the electron will reach the third excited state of energy $- 0.85$ eV, since the energy difference corresponding to $n = 1$ and $n = 4$ is 12.75 eV.

$∴$ $Number of spectral lines emitted = \frac{n (n - 1)}{2} = \frac{4 (4 - 1)}{2} = 6$

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