One of the lines in the emission spectrum of $$L{i^{2 + }}$$ has the same wavelength as that of the Ist line of Lyman series in hydrogen spectrum. The electronic transition corresponding to this line is $$n = 6 \to 3 = x.$$ Find the value of $$x.$$
A.
8
B.
3
C.
7
D.
5
Answer :
3
Solution :
For Ist line of Lyman series in hydrogen spectrum
$$\frac{1}{\lambda } = R\left( 1 \right)\left( {\frac{1}{{{1^2}}} - \frac{1}{{{2^2}}}} \right) = \frac{3}{4}R$$
For $$L{i^{2 + }}\left[ {\frac{1}{\lambda } = R \times 9\left( {\frac{1}{{{3^2}}} - \frac{1}{{{6^2}}}} \right) = \frac{{3R}}{4}} \right]$$
which is satisfied by $$n = 6 \to n = 3.$$
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