the following values are the only energy levels of a hypothetical one electron atom:

E6= -2x10^-19J,
E5= -7x10^-19L
E4= -11x10^-19J,
E3= -15x10^-19J
E2= -17x10^-19J,
E1= -20x10^-19J

a: if the electon were in the n = 3 level, what would be the highest frequency and minimum wavelength of radiation that could be emitted?

b: what is the ionization energy in kJ/mol of the atom in its ground state?

1 answer

Highest frequency and lowest wavelength. Small wavelength means highest energy. Emitted means given off. So the electron must fall from the n = 3 to the n = 1 level.
delta E = E3 - E1 = hc/wavelength
Solve for wavelength.

b. For ionization energy that is the energy required to remove the outside electron to infinity where E = 0. Assuming the single electron is in the E = 1 level (the ground state) then delta E = 20 x 10^-19 J. That is for the 1 electron in a single atom. Multiply by 6.02E23 to find for a mole and convert to kJ.