Zeeman effect problem

1. Apr 18, 2013

dinospamoni

1. The problem statement, all variables and given/known data

The red line of the Balmer series in hydrogen has a
wavelength of 656.5 nm. Suppose that this line is observed to
split into three diﬀerent spectral lines when placed in a magnetic ﬁeld, B, due to the Normal Zeeman Eﬀect. What is the
value of the magnetic ﬁeld if the wavelength splitting between

2. Relevant equations

$\mu_{B}\ =\ 9.27400899(37)\ \times\ 10^{-24}\ J\ T^{-1}$

$E=E_0+\mu_B\times B\times m_l$

3. The attempt at a solution

I said that E - E0 = .065 nm

and solved for B, saying m_l = 1, but that's not right.

Any ideas?

2. Apr 18, 2013

Staff: Mentor

E is an energy, nm is a length and not an energy. You can convert the wavelength values to energy values, then it will work.

3. Apr 18, 2013

dinospamoni

Ah right good catch. I tried that and got 3.3*10^8 T, but that was wrong too.

i did $E = \frac{hc}{\lambda}$

where $\lambda$ is .065 nm

than divided by $\mu_B$

4. Apr 18, 2013

TSny

Note that $E = \frac{hc}{\lambda}$ does not imply that $\Delta E = \frac{hc}{\Delta \lambda}$.