Question

Rydberg has given the equation for all visible radiation in the hydrogen spectrum as $\lambda =\frac{kn^{2}}{n^{2} - 4}$ . The value of $k$ in terms of Rydberg constant is :

• A. $4R$
• B. $\frac{R}{4}$
• C. $\frac{4}{R}$
• D. $R$

Answer 1

Answer: (C)

$\frac{1}{\lambda }=RZ^{2}\left[\frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}}\right]$
$\frac{n^{2} - 4}{kn^{2}}=R\left[\frac{1}{2^{2}} - \frac{1}{n^{2}}\right]$
$\frac{n^{2} - 4}{k \cdot n^{2}}=R\left[\frac{n^{2} - 4}{n^{2} \cdot 4}\right]$
$\boxed{k = \frac{4}{R}}$