Question 107 of 239

The shortest wavelength of the spectral lines in the Lyman series of hydrogen spectrum is $915 Ã…$. The longest wavelength of spectral lines in the Balmer series will be _____ $Ã…$.

Your answerCheck answer

Show answer and solution▾

Answer: 6588

Shortest, $\frac{\mathrm{hc}}{\lambda}=-13.6\left(\frac{1}{\mathrm{n}_1^2}-\frac{1}{\mathrm{n}_2^2}\right)$
$\lambda \downarrow \mathrm{E} \uparrow ; \frac{\mathrm{hc}}{\lambda_0}=-13.6(1)$
Balmer Series :
$\begin{aligned}
& \frac{\mathrm{hc}}{\lambda_1}=-13.6\left(\frac{1}{2^2}-\frac{1}{3^2}\right) \\
& \frac{\mathrm{hc}}{\lambda_1}=-13.6\left(\frac{1}{4}-\frac{1}{9}\right)
\end{aligned}$
$\begin{aligned} & \frac{\mathrm{hc}}{\lambda_1}=-13.6 \times\left(\frac{5}{36}\right) \\ & \Rightarrow \frac{-13.6 \lambda_0}{\lambda_1}=-13.6 \times \frac{5}{36} \\ & \lambda_1=\frac{\lambda_0 \times 36}{5}=\frac{915 \times 36}{5}=6588\end{aligned}$