Transcript lecture26

The Atom
1. The Thomson model (“plum-pudding” model)
It was known that atoms were electrically
neutral, but that they could become charged,
implying that there were positive and negative
charges and that some of them could be
removed.
This model had the atom consisting of a bulk
positive charge, with negative electrons buried
throughout.
Later, Rutherford did an experiment that showed that the positively
charged nucleus must be extremely small compared to the rest of
the atom.
2. Rutherford’s scanning experiment and planetary model
Rutherford scattered alpha particles – helium nuclei – from a metal foil
and observed the scattering angle. He found that some of the angles
were far larger than the plum-pudding model would allow.
Rutherford’s (planetary)
model:
The only way to account for the large angles was to assume that all
the positive charge was contained within a tiny volume – now we
know that the radius of the nucleus is 1/10000 that of the atom.
3. Atomic line spectra (Key to the structure of the atom)
A very thin gas heated in a discharge tube
emits light only at characteristic frequencies.
An atomic spectrum is a line spectrum – only
certain frequencies appear. If white light passes
through such a gas, it absorbs at those same
frequencies.
4. Hydrogen atom
The wavelengths of electrons emitted from hydrogen have a regular pattern:
1 
 1
 R 2  2 

m n 
1
Lyman series : n  1; m  2,3,...
Balmer series : n  2; m  3,4,...
Paschen series : n  3; m  4,5...
Rydberg constant:
A portion of the complete spectrum of hydrogen.
(The lines cannot be explained by the Rutherford theory.)
5. The Bohr Atom
Bohr proposed that the possible energy states (stationary states) for atomic
electrons were quantized – only certain values were possible. Then the
spectrum could be explained as transitions from one level to another.
1 
 1
 R 2  2 

m n 
1
hf 
1 
 1
 hcR 2  2   E f  Ei

n 
m
hc
En  
hcR
n2
hcR  13.60eV
h  6.62  10 34 J  s  4.14  10 15 eV  s
hc  1243eV  nm
Example:
For H 2 :
E min  ?
E2  ?
21  ?
hcR
13.60eV
En   2  
n
n2
Emin  E1  13.60eV
E2  
13.60eV
 3.40eV
2
2
E  E 2  E1  13.60eV (1  14 )  10.20eV
hc 1243eV  nm

E
10.20eV
  122nm

5a. Stable orbits (The Bohr Atom)
Quantization:
An electron is held in orbit
by the Coulomb force:
r1   0
4
1
me
K n  12 mv  2 2 2
 0 8n h
1 e2
vn 
 0 2nh
h
L  mvn rn  n
2
1 e 2 mvn2

2
40 rn
rn
rn   0
h 2
me
2
 0.529 10
10
nh 2
me2

m  0.529 A
2
e2
1 me4
Un  
 2 2 2
40 rn
 0 4n h
1
1 me4
hcR
En  K n  U n   2 2 2   2 
 0 8n h
n
me4
R  2 3  1.0974 107 m 1
8 0 h c
hcR
13.6eV
En   2  
n
n2
The Bohr Atom
The lowest energy level is called the
ground state; the others are excited states.
Example: Franck- Hertz experiment
Franck and Hertz studied the motion of electrons through mercury vapor
under the action of an electric field. When the electron kinetic energy was
4.9eV or grater, the vapor emitted ultraviolet light. What was the wave length
of this light?
E  4.9eV
 ?
hf 
hc

 E
hc 1243eV  nm


 250nm
E
4.9eV