What is the wavelength of a photon....?

Question

What is the wavelength of a photon needed to excite an electron from (-15 x 10^-19) to (-1.0 x 10^-19)?
I know the first step is to do (-1.0 x 10^-19) - (-15 x 10^-19)
which equals (1.4 x 10^-18).

Answer 1

energy = Planck's constant * frequency

and frequency = speed of light / wavelength

so
energy = Planck's constant * speed of light / wavelength

solve for wavelength:
wavelength = Planck's constant * speed of light / energy

plug the values in and do the calculation. use consistent units.

Answer 2

If those numbers you gave are electron energy levels, then when an electron drops in energy from 15 to 1 X 10^-19 [What are the units here?], it's energy is dissipated by a photon that has photonic energy (15 - 1)X 10^-19 = Del E = hf; where h is Planck's constant and f is the frequency of the photon emitted.

Solve the above for f = Del E/h; where Lf = c, and L is the wavelength and c is light speed. Thus L = c/f = c/(Del E/h) will get you your answer.

Notice, the photon is emitted when the energy level goes down. That is you don't insert a photon to "excite" an electron to a lower level of energy. The emitted photon is the excess energy the electron had to slough off to get to the lower level.

What we just described is called the Zeeman Effect. In the lab, electrons are excited by strong magnetic forces and when the excited electrons revert to their natural energies levels, they emit the light that can be analyze through spectrographs.