Please help me to understand how to work this problem: Calculate the energy of a photon emitted when an electron in a hydrogen atom undergoes a transition from n = 4 to n = 1.

Question

doc.brown · Answer

An electron lives happily in its orbital.  You can give it enough energy to hop it up to the next orbital by shooting light at it.  The energy you give it doesn't depend on the intensity of the light, but rather the color.  Thanks Einstein.  And energy moves about the universe in tiny packages.  Thanks Planck.  So to lift an electron from the first orbital n1 to the second n2, you need a certain color wave packet.  Photon.
When the electron drops back from n2 to n1 it shoots off exactly the same amount of energy.  Exactly.  A photon of the exact same color.
A drop from the fourth orbital n4 gives a larger amount of energy. A photon with a higher frequency.

doc.brown · Answer

$$E=Energy$$$$h=Plancks~constant=6.626\times10^{-34}J\cdot s$$$$v=frequency$$$$E=hv$$For hydrogen use the formula$$E=-13.6[\frac{1}{n_1^2}-\frac{1}{n_2^2}]eV$$$$E=-13.6[\frac{1}{1^2}-\frac{1}{4^2}]eV$$$$E=12.8eV$$

anonymous · Answer

ok..I see thanks so much