# Problem: Hydrogen gas absorbs light of wavelength 103nm. Afterward, what wavelengths are seen in the emission spectrum?

###### FREE Expert Solution

Energy of absorbed photon:

$\begin{array}{rcl}\mathbf{E}& \mathbf{=}& \frac{\mathbf{h}\mathbf{c}}{\mathbf{\lambda }}\\ & \mathbf{=}& \frac{\mathbf{\left(}\mathbf{6}\mathbf{.}\mathbf{626}\mathbf{×}{\mathbf{10}}^{\mathbf{-}\mathbf{34}}\mathbf{\right)}\mathbf{\left(}\mathbf{3}\mathbf{×}{\mathbf{10}}^{\mathbf{8}}\mathbf{\right)}}{\mathbf{103}\mathbf{×}{\mathbf{10}}^{\mathbf{-}\mathbf{9}}}\end{array}$

E = 1.93 × 10-18J = (1.93 × 10-18)/(1.6 × 10-19) = 12.06 eV

After absorbing this photon, hydrogen undergoes a transition to a higher state n with energy (-13.6/n2) from the ground state that initially had the energy  (-13.6/12)

To get n:

[(-13.6/n2) -  (-13.6/12)] = 12.06

13.6/n2 = 1.54

n = sqrt (13.6/1.54) = 3.

90% (242 ratings) ###### Problem Details

Hydrogen gas absorbs light of wavelength 103nm. Afterward, what wavelengths are seen in the emission spectrum?