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rtareen

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- TL;DR Summary
- Attached is a problem from my Book (Young & Freedman University Physics 14E), where they are softly claiming that if an electrons orbital quantum number goes down, then it loses energy. This is completely new to me as before we were told that the energy only depends on the principal quantum number.

In Example 41.5, they are implying that, for a hydrogen atom, if the orbital quantum number ##l## goes down the electron will lose energy. However, they said nothing about the principal quantum number ##n## going down, so there should be no loss in energy. As far as this book has presented, the energy only depends on the principal quantum number, but now they are saying it will lose energy if the orbital quantum number goes down. In fact, the energy level equation they gave was

##E_{n} = -\frac{1}{(4\pi \epsilon_0)^2} \frac{m_rZ^2e^4}{2n^2\hbar^2} = -\frac{(13.60~\text{eV})Z^2}{n^2} ##

I know its losing energy because that's how the photon is emitted. Can somebody explain this?Also, does Zeeman splitting just mean that for a given ##n##, the single energy level becomes split into multiple energy levels given by

##E_n + U(m_l)##?

So if ##(n,l) = (2,1)## then the single energy level is split into three? Particularly

##E_2 + U(-1)## and ##E_2 + U(0)## and ##E_2 + U(1)##

Is that right?

##E_{n} = -\frac{1}{(4\pi \epsilon_0)^2} \frac{m_rZ^2e^4}{2n^2\hbar^2} = -\frac{(13.60~\text{eV})Z^2}{n^2} ##

I know its losing energy because that's how the photon is emitted. Can somebody explain this?Also, does Zeeman splitting just mean that for a given ##n##, the single energy level becomes split into multiple energy levels given by

##E_n + U(m_l)##?

So if ##(n,l) = (2,1)## then the single energy level is split into three? Particularly

##E_2 + U(-1)## and ##E_2 + U(0)## and ##E_2 + U(1)##

Is that right?