In: Chemistry
what is the wavelength of the longest wavelength photon that a Ground state hydrogen atom can absorb?
The electron in a ground state hydrogen atom is in n = 1 state. when a ground state hydrogen atom absorb a photon it will move to n = 2 state
One way to do this is to first calculate the energy of the electron in the initial and final states using the equation:
En = (-13.6 eV)/n2
E2 = (-13.6 eV)/4 = -3.4 eV
E1 = (-13.6 eV)/1 = -13.6 eV
In moving to n = 2 state from the ground state the electron 10.2 eV worth of energy required. This is the energy given by the photon.
Converting this to joules gives E = 10.2 * 1.60 x 10-19 J/eV = 1.632 x 10-18 J
For a photon E = hf = hc/λ
λ = hc/E = 6.63 x 10-34 * 3 x 108 / 1.632 x 10-18
λ = 1.22 x 10-7 m = 122 nm
so a photon of 122 nm wavelength will be absorbed by ground state hydrogen