Question

Hydrogen gas absorbs light of wavelength 103 nm. Afterward, name the longest wavelength seen in the emission spectrum in nm?

Answer 1

The wavelengths which are absorbed by the hydrogen atom are all multiples of the fundamental radius, which is a0=0.0529nm. A wavelength of 103nm corresponds to:

$n_{\lambda}=\frac{\lambda}{6.28*a_0}=\frac{103*10^{-9}}{6.28*0.0529*10^{-9}}\approx310$

So the next will be 311, which correspondes to a wavelength of:

$\lambda=6.28*311*0.0529*10^{-9}=103.318nm$

Thus, our answer is lambda=103.318nm