Question

Calculate the frequency and wavelength of the radiation in nm emitted when an electron in hydrogen atom jumps from third to ground state .

Answer 1

Dear Student,
GIVEN: n_i=3 , n_f= 1

$∆E=R_H(\frac{1}{n_i^2}-\frac{1}{n_f^2})$

$$\begin{gathered} ∆E=2.18\times {10}^{-18}(\frac{1}{3^2}-\frac{1}{1^2}) \\ ∆E=2.18\times {10}^{-18}\times \frac{1}{9} \end{gathered}$$
$∆E=2.42\times {10}^{-19}J$
we know that
$∆E=h\nu$
frequency $\nu =\frac{2.42\times {10}^{-19}}{6.62\times {10}^{-34}}=3.6\times {10}^{14}Hz$
$$\begin{gathered} ∆E=\frac{hc}{\lambda } \\ wavelength\lambda =\frac{6.62\times {10}^{-34}\times 3\times {10}^8}{2.42\times {10}^{-19}} \end{gathered}$$

$\lambda =8.2\times {10}^{-7}m0r820nm$