Atomic physics: sodium D-line transition missing 2 pi

[El Hombre Invisible]

Homework Statement

Find the wavelength of the sodium transition [tex]3p^{1},^{2}P -> 3s^{1},^{2}S[/tex]

Homework Equations

[tex]E_{n,l} = -\frac{hcR}{(n - d(n,l))^{2}}[/tex]

d(3,s) = 1.374
d(3,p) = 0.884

[tex]\lambda = \frac{\hbar c}{\Delta E}[/tex]

The Attempt at a Solution

Plugging the numbers in ain't even close. However, I've found another equation that works:

[tex]\frac{1}{\lambda} = -R[\frac{1}{(n_{i} - d_{i}(n,l))^{2}} - \frac{1}{(n_{f} - d_{f}(n,l))^{2}}][/tex]

but since E is proportional to [tex]\hbar[/tex] and the RHS on the top equation just to h... where did the [tex]2\pi[/tex] go..?

 

[El Hombre Invisible]

'Sokay. Just realized [tex]\lambda = \frac{hc}{\Delta E}[/tex] not [tex]\frac{\hbar c}{\Delta E}[/tex]. Knew it would be something stupid.