Single Choice

One of the lines in the emission spectrum of $$Li^{2+}$$ has the same wavelength as that of the $$2^{nd}$$ line of Balmer series in hydrogen spectrum. The electronic transition corresponding to this line is $$n = 12\rightarrow n = x$$. Find the value of $$x$$.

A$$8$$
B$$6$$
Correct Answer
C$$7$$
D$$5$$

Solution

For $$2^{nd}$$ line of Balmer series in hydrogen spectrum $$\dfrac {1}{\lambda} = R(1) \left (\dfrac {1}{2^{2}} - \dfrac {1}{4^{2}}\right ) = \dfrac {3}{16}R$$ For $$Li^{2+}\left [\dfrac {1}{\lambda} = R \times 9\left (\dfrac {1}{x^{2}} - \dfrac {1}{12^{2}}\right ) = \dfrac {3R}{16}\right ]$$ Which is satisfied by $$n = 12\rightarrow n = 6$$.

SIMILAR QUESTIONS

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