Question

In a certain one-electron atom, the longest wavelength at which the atom in its
ground state can absorb a photon is 7.598 nm. What is the next longest
wavelength at which a photon can be absorbed from the ground state of this atom?

Answer 1

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:

E_n = (-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^-19J/eV = 1.632 x 10^-18 J

For a photon E = hf = hc/?

? = hc/E = 6.63 x 10^-34 * 3 x 10⁸ / 1.632 x 10^-18

? = 1.22 x 10^-7 m = 122 nm

so a photon of 122 nm wavelength will be absorbed by ground state hydrogen