# Determinining the wavelength and color of an atom of X

Well, the real subject title should be: determining the wavelength and color of radiation emitted when an atom of X undergoes a transition from lowest excited state to the ground state.

Alrighty... What do we know? The energy needed to ionize an atom of element X when it is in its ground stat is 500 KJ/mol.
The energy needed to ionize an atom of element X in its lowest excited state is only 120 KJ/mol.

How do we find the wavelength?

I considered using Rydberg's equation to determine the wavelength but the equation only works for hydrogen. :( I'm really lost. Please help!

### Re: Determinining the wavelength and color of an atom of X

shengoc Sat, 02/20/2010 - 06:54

goosegirl13 wrote:

Well, the real subject title should be: determining the wavelength and color of radiation emitted when an atom of X undergoes a transition from lowest excited state to the ground state.

Alrighty... What do we know? The energy needed to ionize an atom of element X when it is in its ground stat is 500 KJ/mol.
The energy needed to ionize an atom of element X in its lowest excited state is only 120 KJ/mol.

How do we find the wavelength?

I considered using Rydberg's equation to determine the wavelength but the equation only works for hydrogen. :( I'm really lost. Please help!

If you sketch out the two energy level between ground state and the excited state, you'd find that the energy separation between them is 500 - 120 = 380 kJ/mol
But since you are dealing with an atom, so you'd need to divide this number by the avogadro's constant.

Then when dealing with spectroscopy question, always remember delta E = hf = hc/lambda
f is frequency of the radiation, and with simple manipulation, you get the second eqn, lambda is the wavelength of the radiation, that is what you want to find.