First slide

Hydrogen -like ion

Question

Hydrogen atom in ground state is excited by a monochromatic radiation of $λ$ = 975 $\overset{ο}{A}$ . Number of spectral lines in the resulting spectrum emitted will be

Moderate

A

3
B

2
C

6
D

10

Solution

$Energy of the photon, E = \frac{h c}{λ}$
$E = \frac{6.63 \times 10^{- 34} \times 3 \times 10^{8}}{975 \times 10^{- 10}} J$
$= \frac{6.63 \times 10^{- 34} \times 3 \times 10^{8}}{975 \times 10^{- 10} \times 1.6 \times 10^{- 19}} eV = 12.75 eV$
After absorbing a photon of energy 1275 eV, the electron will reach to third excited state of energy-0.85 eV, since 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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