set the stage for Bohr’s orbital model of the atom, which utilized the
idea of a central nucleus.
Niels Bohr realized that Rutherford’s model developed by his scattering
experiment only explained the scattering effect and did not present an
answer to any of these problems:
1. How are the electrons arranged about the atom?
2. What keeps the negative electron from falling into a positive
nucleus by electrical
3. What allows the Balmer formula for hydrogen admission and
absorption spectral lines to
4. Of what is the nucleus composed?
5. What keeps the nucleus from exploding on account of the repulsion
of its positive
Niels was able to answer the first three questions in his first model
it in VRML!
The two postulates of this model stated:
1. Electrons in the atom can exist in stationary states which
emit no radiation.
2. The emission and absorption of radiation is explained by a
between these stationary states. The
frequency of the emitted or absorbed radiation
is modeled by the equation hf = Ei - Ef where
h is Planck’s constant, f is the frequency,
and Ei and Ef are approximately the energies
of the atom in the initial and final stationary
Bohr calculated an equation for his model that gave simplistic values
for the radii at which the electrons could orbit. The equation was
rn = an2 where a is the constant h2/4?2mkqe ( 5 X 10-11 m )
and n was any integer except zero. This model now theorized how the
electrons were arranged about the atom.
The first postulate allowed the electron to defy classical physics because
old school states that a body such as the electron would radiate energy
when moving in a planetary motion, which would cause the electron to be
pulled in in less than a second. Since there is no energy being emitted
when the electron is in this “stationary state” it is able to move about
like the moon does to earth without crashing into Australia like a space
station. This postulate also supports Robert Millikan’s Oil Drop
experiment in that it explains how an atom can exist only in definite amounts
of quanta, hence “stationary states.”
The second postulate explains how the atom can have varying values of
quanta caused by the absorption or admittance of electromagnetic radiation
( light. ) The transitional stage between the stationary states is
discontinuous or non existent. The overall charge of the atom either
increases or decreases to a minimum when the electron jumps from one stationary
state to another. The jump is caused by a quantized radiation that
hits the atom and transfers the electron to another stationary state.
This occurrence can be modeled by Bohr’s equation as seen above hf = Ei
- Ef .
The Balmer formula is an empirical relation that determines the wavelength
of light from spectral lines emitted by an element or elements. What
is most striking about the Bohr model is that it can be derived into the
Balmer formula. It looks like this
Balmer formula: 1 = RH X 1
- 1 Bohr formula: hf = Ei - Ef
If the quantum number is n, Ef = 1 E1 and Ei = 1 E1 where
E1 is the energy of the atom in the first orbit.
Substituting each into Bohr’s Formula we get hf = E1 X 1 - 1
Next substitute c /
for f: hc = E1 X 1 - 1
Divide both sides by Plank’s constant h times the speed of light c:
1 = E1 X 1 - 1
hc n2i n2f
RH is Ryberg’s constant which turns out to be equal to (-E1/ hc ), so
= RH X 1 -l