One of the lines in the emission spectrum of \(\text{Li}^{2+}\) has the same wavelength as that of the second line of the Balmer series in hydrogen spectrum. The Balmer transition corresponds to \(n=4\rightarrow2\). If the corresponding transition in \(\text{Li}^{2+}\) is \(n=12\rightarrow x\), find the value of \(x\).
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For hydrogen-like ions:
\[
\lambda\propto\frac{1}{Z^2}
\]
Higher \(Z\) compresses the spectrum.