How Is the Magnetic Field Calculated in the Normal Zeeman Effect?

[dinospamoni]

Homework Statement

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
adjacent lines is 0.065 nm?

Homework Equations

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

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

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?

 

[mfb]

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.

 

[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

 

[TSny]

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