Question

For emission line of atomic hydrogen from ${\text{n}}_i=8to{n}_f=n$, the plot of wave number ($\stackrel{-}{v}$) against $\frac{1}{n^2}$will be (The Rydberg constant $R_H$ is in wave number unit)

• A. Linear with slope -$R_H$
• B. Linear with intercept -$R_H$
• C. Non-linear
• D. Linear with slope $R_H$

Answer 1

The correct option is D Linear with slope $R_H$

We know that,
$\frac{1}{\lambda }=\stackrel{-}{v}=R_H{Z}^2(\frac{1}{n_1^2}-\frac{1}{n_2^2})$
$\stackrel{-}{v}=R_H{1}^2(\frac{1}{n_1^2}-\frac{1}{8^2})$
$\stackrel{-}{v}=R_H(\frac{1}{n_1^2}-\frac{1}{8^2})$
$\stackrel{-}{v}=R_H\frac{1}{n_1^2}-\frac{R_H}{8^2}$
Comparing above equation with $y=mx+c,m=R_H$