First slide

Hydrogen spectrum

Question

An electron jumps from the fourth orbit to the second orbit of hydrogen atom. Given: the Rydberg's constant $R = 10^{5} {cm}^{- 1}$ . The frequency, in Hz, of the emitted
radiation will be

Moderate

A

$\frac{3}{16} \times 10^{5}$
B

$\frac{3}{6} \times 10^{15}$
C

$\frac{9}{16} \times 10^{5}$
D

$\frac{9}{16} \times 10^{15}$

Solution

$\begin{array}{rcl} \frac{1}{λ} & = & R [\frac{1}{2^{2}} - \frac{1}{4^{2}}] \\ or \frac{f}{c} & = & R [\frac{1}{4} - \frac{1}{16}] \\ or f & = & c R [\frac{1}{4} - \frac{1}{16}] = 3 \times 10^{8} \times 10^{7} \times \frac{3}{16} \\ = & \frac{9}{16} \times 10^{15} Hz \end{array}$

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