Page 228 - Essentials of physical chemistry

190 Essentials of Physical Chemistry

or

12398:41906
DE (eV) ¼
l (A ˚ )
and more generally useful as

12,398
:
DE (eV) ffi
l (A ˚ )
This was first brought to our attention many years ago [4] and has proved to be very useful for quick
estimates of wavelength or energies in electron volts doing mental arithmetic while sipping coffee in
a seminar.

PRELIMINARY SUMMARY OF THE BOHR ATOM

2
2
n 12,398 Z
; (13:6057 eV)
Z l (A ˚ ) n
r(n, Z) ¼ (0:5291772 A ˚ ); DE (eV) ffi E(n, Z) ¼
These three formulas can be used for quite a few applications which will be our introduction to
spectroscopy. The most obvious application is to compare the energy formula to the experimental
wavelengths of the H atom spectrum (Z ¼ 1):

1 1 hc
DE (eV) ¼ E 2 E 1 ¼ ( 1) (13:6057 eV) ¼
n 2 n 2 l
2 1
This has the same type denominator as the Balmer formula and when the other numbers are
compared, it is found that the Bohr equation is essentially the same as the Balmer equation.
There is only a slight difference due to the fact that the nucleus in the Bohr model is fixed at the
center of the atom while the real spectra include the fact that the electron and proton both orbit
around the center-of-mass (the see-saw balance point) of the two particles. That is really very close
to the position of the proton because it is much more massive than the electron. When this correction
is made to the Bohr formula, the agreement with the experimental spectra is essentially exact.
One other unit we may encounter in spectroscopy, particularly in infrared spectroscopy, is the
‘‘wave number.’’ Basically, the wave number is just the reciprocal of the wavelength:

c ¼ ln

so

c
n ¼
l
and

1
n
l c
n ¼