What is the Role of Magnetic Fields in Allowing Electron Transitions?

[dachikid]

Hi All,

I'm a bit confused about electron transitions. I'm hoping someone will be willing to straighten me out. So the problem at hand states that a single ionized Helium atom has its single electron in the 5d shell. The z component of this electron's orbital angular momentum is $$\hbar$$ and its spin angular momentum is $$+\frac{1}{2}\hbar$$.

Now if the electron is initially in the ground state (i.e. 1s) what would be needed to get it to the 5d subshell?

So my initial thoughts are inclined to think that the electron must be given energy, possibly a photon. This energy would have a value of $$-E_0(\frac{1}{5^2} - \frac{1}{1^2})$$ where $$E_0=-13.6ev$$

Because photons carry angular momentum, $$l$$ the orbital angular momentum of the electron must change in increments of $$\Delta l= \frac{+}{-}1$$ due in part to the "selection rule"

So a transition from a (1s) state $$\frac{n}{1} \frac{l}{0} \frac{m_l}{0} \frac{m_s}{\frac{+}{-}1}$$ to a (5d) state $$\frac{n}{5} \frac{l}{2} \frac{m_l}{1} \frac{m_s}{\frac{+}{-}1}$$ is not possible because $$\Delta l =2$$

Now if I throw the atom in a magnetic field, the selection rule for $$\Delta m_l=0,\frac{+}{-}1$$ says the transition is allowed because $$\Delta m_l = +1$$, I think

So just introducing a magnetic field allows a transition, which is not normally allowed, to be allowed?

thanks in advanced for any help!

 

[genneth]

Why not try two photons?

 

[pam]

So a transition from a (1s) state $$\frac{n}{1} \frac{l}{0} \frac{m_l}{0} \frac{m_s}{\frac{+}{-}1}$$ to a (5d) state $$\frac{n}{5} \frac{l}{2} \frac{m_l}{1} \frac{m_s}{\frac{+}{-}1}$$ is not possible because $$\Delta l =2$$

$$\Delta L=2$$ is possible for quadrupole absorption.
Expand the incident EM plane wave into multipoles.