What was the formula that Balmer found?
Balmer examined the four visible lines in the spectrum of
the hydrogen atom; their wavelengths are 410 nm, 434 nm, 486 nm,
and 656 nm. He played around with these numbers and eventually
figured out that all four wavelengths (symbolized by the Greek
letter lambda) fit into the equation|
R is a constant, called the Rydberg
The number n is just an integer; the above
the longest wavelength, 656 nm, when n=3, and gives each of
the shorter wavelengths as n increases up
656 nm is the red line in that picture, right?
Correct; the shorter wavelengths correspond to the blue and violet
lines you can see. (The 410 nm line is very faint, but it's there
if you look closely.) This set of lines was called the Balmer
series. Later, other researchers found that the series could
be extended into ultraviolet wavelengths; the same formula still
worked, with larger values of n.
Hmm...from Balmer's equation, it looks like when n gets
lines should start getting really close together.
That's exactly right; as n gets larger, 1 over n
squared gets smaller, so there's less and less difference between
the consecutive lines. You can see that the series has a limit--
that is, as n gets larger and larger, the wavelength gets
closer and closer to one particular value. If n is
infinity, then 1 over n squared is 0, and if you work out
the numbers, you'll find that the wavelength is about 365
nm. That's just what experimentalists saw; around 365 nm, the
lines became too close together to distinguish.
So do all of the emission lines from a hydrogen atom fit somewhere
into the Balmer series?
No, they don't. As scientists looked further into the non-visible
parts of the spectrum, they found other series--which obeyed
formulas hauntingly similar to Balmer's. For example, the
series, which is entirely in the ultraviolet, fits the
And the lines of the Paschen series,
in the infrared,
Those integers have got to have something to do with Bohr's energy
Yes, they do; I'll show you how Bohr was able to deduce the
electron's angular momentum from this formula...