Rutherford’s Atom
A Miniature Solar System
Atomic Spectra
Atoms exhibit sharp emission lines
instead of continuous distributions.
Absorption lines are at the same wavelengths
as emission lines.
Emission lines for
hydrogen are at
 1
1
= R 2 − 2 
λ
 n f ni 
where n f < ni .
1
Rydberg constant:
R = 1097
.
× 10 7 m −1 .
Lyman Series: n f = 1
Balmer Series: n f = 2
Paschen Series: n f = 3
Bohr Model of the Hydrogen Atom
1. Electrons move in circular orbits around proton under
attraction of Coulomb force.
ke 2 me v 2
FE = ma c gives
Using
.
2 =
r
r
2
2
ke
ke
ke
Which means PE = −
, KE = 21 me v 2 =
,E = −
.
2r
2r
r
2
2. Radiation is emitted when an electron jumps to a lower
energy orbit, E i − E f = hf = hc / λ .
3. Only certain orbits (radii) are stable, L = me vr = nh / 2π .
This implies that
where
ke 2
E= − 2
2n a 0
and
r = n a0
2
h2
− 11
a0 =
=
.
×
m = 0.0529nm .
5
29
10
2
2
4π me ke
This would also work for the atoms other than hydrogen if we
assume the electrons don’t affect each other.
Angular Momentum is quantized: Ln = me vr = nh / 2π
Radii if orbits are quantized: rn = a 0 n 2 / Z
ke 2 Z 2
Energy Levels are quantized: E n = −
2a 0 n 2
2
Z
E n = − (2.18 × 10 −18 J ) 2
n
Z2
E n = − (13.6eV ) 2
n
If electrons are waves,
orbits are only stable
if they result in
constructive
interference.
Since they can travel
either direction, they
must produce standing
waves.
2πr = nλ = nh / m e v
m e vr = nh / 2π
X-rays