Question

For emission line of atomic hydrogen from $n_i = 8$ to $n_f $ = the plot of wave number $(\bar{v})$ 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

Answer: (D)

$\frac{1}{\lambda} = \bar{V} = R_{H} Z^{2} \left(\frac{1}{\eta^{2}_{1}} - \frac{1}{\eta^{2}_{2}}\right) $
$ \bar{V} = R_{H} \times \left(\frac{1}{\eta^{2}_{1}} - \frac{1}{8^{2}}\right) $
$\bar{V} = R_{H} \times\frac{1}{\eta^{2} } - \frac{R_{H}}{8^{2}} $
$\bar{V} = R_{H} \times \frac{1}{\eta^{2} } - \frac{R_{H}} {64} $
$m = R_{H} $
Linear with slope $R_H$