Determine the wavelength of the radiation emitted by hydrogen...

The wavelength of the emitted radiation is given by the Rydberg formula:

$\dfrac{1}{\lambda} = R_H \left( \dfrac{1}{n_1^2} - \dfrac{1}{n_2^2} \right)<br><br>Given$n_1 = 9$,$n_2 = 10$, and Rydberg constant$R_H = 1.097 $\times$10^7 $\text{ m}^{-1}:<br><br>\dfrac{1}{\lambda} =$1.097 $\times$10^7 \left( \dfrac{1}{9^2} - \dfrac{1}{10^2} \right)$<br><br>$\dfrac{1}{\lambda} = 1.097 \times 10^7 \left( \dfrac{1}{81} - \dfrac{1}{100} \right)

\dfrac{1}{\lambda} =$1.097$\times$10^7 \left( \dfrac{19}{8100} \right)$

$\lambda = \dfrac{8100}{19 \times 1.097 \times 10^7} \text{ m}$

$\lambda = \dfrac{8100}{20.843 \times 10^7} \text{ m}$

$\lambda \approx 388.62 \times 10^{-7} \text{ m}$

$\lambda \approx 38862 \text{ nm}$

The closest value among the given options is $38860 \text{ nm}$.