Question

Light shines through atomic Hydrogen gas. It is seen that the gas absorbs light readily at a wavelength of 91.65 nm. What is the level to which the Hydrogen is being excited by the absorption of light of this wavelength? Assume that most of the atoms in the gas are in the lowest level.

Answer 1

Answer:

n = 19

Explanation:

$\lambda$ = Wavelength of the light absorbed = 91.65 nm = 91.65 x 10⁻⁹ m

$n_{2}$ = nth level = n

$n_{1}$ = 1

Using conservation of energy

$\frac{hc}{\lambda} = (13.6\times1.6\times10^{-19}) (\frac{1}{n_{1}^2} - \frac{1}{n_{2}^2} )\\\frac{(6.63\times10^{-34})(3\times10^{8})}{(91.65\times10^{-9})} = (13.6\times1.6\times10^{-19}) (\frac{1}{1^2} - \frac{1}{n^2} )\\2.17\times10^{-18} = (21.76\times10^{-19}) (\frac{1}{1^2} - \frac{1}{n^2} )\\n = 19$