Color Photon

Calculate the wavelength of the emitted photon?

If an electron makes a transition from the third principal energy level (n=3) to the second principal energy level (n=2), calcuate the wavelength of the emitted photon. Then determine the photon’s color.

Depends on what kind of atom you have, but if you are talking about hydrogen,
we can find the wavelength (w) from Rydberg’s equation, 1/w = R(1/L² – 1/U²)
where L is the lower energy level (in this case 2) and U is the upper level (3)
and R is the Rydberg constant, experimentally determined as 10,967,758 waves
per meter for hydrogen. So if L = 2 and U = 3, we can find w by substituting and
we obtain: 1/w = 10967758(¼ – 1/9) = 10967758(0.25 – 0.1111) = 1,523,299
So the wavelength w = 1/1523299 = 6.564 * 10**-7 meter, or 656.4 nanometers.
This is in the visible range as red light. It’s also called the Hydrogen-α line in
the Balmer (visible) hydrogen spectrum.
Hope this answers your question.

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