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2023-01-01

What is the series limit for the Balmer series? (The series limit, like the name suggests, is the last line of the given series - the smallest wavelength that's still part of the same set of spectral lines)
A. 364.6nm
B. 121.6nm
C.656.3nm
D. 385.4nm

Keely Franco

Expert

Rydberg is our knight in shining armour, again! We know, for the Balmer series ${n}_{1}=2$. The series limit, or the very last line in the series, will be obtained by putting ${n}_{2}=\mathrm{\infty }$. Thus the Balmer series limit can be found as –
$\frac{1}{{\lambda }_{\mathrm{\infty }}}=R\left(\frac{1}{{2}^{2}}-\frac{1}{{\mathrm{\infty }}^{2}}\right)=\frac{R}{4}{m}^{-1}$
}\Rightarrow \lambda_\infty=\frac4Rm=3.646\times10^{−7}m=364.6nm.Show External URL Show Embeded Code Hide MathML Code⇒λ∞=4Rm=3.646×10−7m=364.6nm.$⇒{\lambda }_{\mathrm{\infty }}=\frac{4}{R}m=3.646×{10}^{-7}m=364.6nm.$
Option (a) is correct!

The significance of the wavelength is, it’s the Balmer line with the smallest wavelength. The next line with a smaller wavelength will be the first line of the Lyman series, which is 121.6 nm. This essentially means, there will be no spectral lines in the range 121.6 nm - 364.6nm.

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