Exciting an electron in a hydrogen atom.

[weston_sagle]

Homework Statement

A hydrogen atom in its ground state is illuminated with light having a wavelength of 96.7 nm. can the hydrogen atom's electron be excited to a higher energy state by absorbing one of these photons? If so, determine the state and wavelength of any photon that would be emitted by the atom.

Homework Equations

E=hc/lambda
En=-13.6eV/n^2

The Attempt at a Solution

E=hc/lambda
=[(6.626x10^-34)(3.0x10^8)/9.67x10-8]
=2.0556x10^18 J

Convert to / by 1.602x10^-19 eV = 12.83eV

En=-13.6eV/1^2 = -13.6eV

So I think that the photon energy would have to exceed 13.6eV to excite the electron, so in this case it would not excite it. Is this right?

 

[member 553083]

If it did excite the electron, would the wavelength of the photon emitted be longer or shorter than the one absorbed? Would the energy of the emitted photon be greater or less than that of the absorbed photon?