Question

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. 364.6 nm
• B. 121.6 nm
• C. 656.3 nm
• D. 385.4 nm

Answer 1

The correct option is A 364.6 nm

Rydberg is our knight in shining armour, again! We know, for the Balmer series $n_1=2$. We will obtain the series limit, or the very last line in the series (lowest wavelength), by putting $n_2=\infty$. Thus the Balmer series limit can be found as –

$\frac{1}{{\lambda }_{\infty }}=R(\frac{1}{2^2}-\frac{1}{{\infty }^2})=\frac{R}{4}{m}^{-1}$
$\Rightarrow {\lambda }_{\infty }=\frac{4}{R}m=3.646\times {10}^{-7}m=364.6nm.$
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.