In L i ++ ,electron in first Bohr orbit is excited to a level by a radiation of wavelength λ .When the ion gets de excited to the ground state in all possible ways (including intermediate emissions),

Question

In L i ++ ,electron in first Bohr orbit is excited to a level by a radiation of wavelength λ .When the ion gets de excited 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 × 1 0 − 34 J s ; c = 3 × 1 0 8 m s − 1 )

TestHub · Accepted Answer

Total Number of possible spectral lines that can be emmited when atom de-excites from state $n$ to groundstate is $_^{n} C_{2}$

$∴^{n} C_{2} = 6 \Rightarrow \frac{n ( n - 1 )}{2} = 6 \Rightarrow n = 4$

$\frac{1}{λ} = R z^{2} (\frac{1}{1 ^{2}} - \frac{1}{4 ^{2}}) = 1.097 \times 1 0^{7} \times 9 \times (1 - \frac{1}{16})$

$\Rightarrow λ = 10.8 nm$

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