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Hydrogen Spectra

In Li++, el...

Question

In $L i^{+ +}$ , electron in first Bohr orbit is excited to a level by a radiation of wavelength $λ$ . when the ion gets deexcited to the ground state in all possible ways (including intermediate emissions), a total of six spectral lines are observed. What is the value of $λ$ ?
(Given : $h = 6.63 \times 10^{34} J s$ ; $c = 3 \times 10^{8} m s^{- 1}$ )

A

9.4 n m

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B

12.3 n m

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C

10.8 n m

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D

11.4 n m

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Solution

The correct option is C $10.8 n m$
$Δ E = \frac{h c}{λ}$
$13.6 \times 9 - 0.85 \times 9 = \frac{h c}{λ}$
$λ = \frac{h c}{9 \times (13.6 - 0.85) e V}$
$= \frac{1240 e V . n m}{9 \times 12.75 e V}$
$λ = 10.8 n m$

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