Question

What is the energy difference between the two quantum states involved in the transition of red light with wavelength 705 nm being absorbed by an atomic gas?

Answer 1

I found:
`E=h*nu=2.82xx10^-19J=1.76eV`

Explanation:

A wavelength of `705 nm` corresponds to a frequency:
`nu=c/lambda=(3xx10^8)/(7.05xx10^-7)=4.25xx10^14Hz`

From Einstein's Relatonship you have that the photon energy will be:

`color(red)(E=h*nu)=6.63xx10^-34*4.25xx10^14=2.82xx10^-19J=1.76eV`

This is exactly the energy gap (or difference) between the two quantum states involved in the absorption of your photon of red light.