What wavelength photon would be required to ionize a hydrogen atom in the ground state and give the ejected electron a kinetic energy of 13.1 eV?

Question

I tried ryhdberg's equation and E=hf. Need help.

Thanks

Answer 1

The ground state of a hydrogen atom is 13.6 eV below the ionization threshold. If the free electron is to have 13.1 eV of kinetic energy, the total energy needed is 26.7 eV. Convert that to photon energy E in Joules using 1.6*10^-19 J per eV. Then use the Planck relationship
E = h c/L, where L is the wavelength in meters and h is Planck's constant, to solve for L.