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 × 10 - 34 J s ; c = 3 × 10 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 ${}^{n}C_{2}$
$∴^{n} C_{2} = 6 \Rightarrow \frac{n (n - 1)}{2} = 6 \Rightarrow n = 4$
$\frac{1}{λ} = R z^{2} (\frac{1}{1^{2}} - \frac{1}{4^{2}}) = 1.097 \times 10^{7} \times 9 \times (1 - \frac{1}{16})$
$\Rightarrow λ = 10.8 n m$

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