Download Atomic Physics

By C K Cheung
Atomic Physics
Matter ----- composed of atoms and molecules.
Atom ----- composed of ??????
J.J. Thomson Experiment (1897 )
Thomson’s ‘ plum – pudding ‘model of atoms:
electron
+ve charged matter spread
uniformly over the entire region
10 – 10 m
Rutherford Scattering Experiment (1910)
Thin gold
foil ~10 –7m
Pb shield

< 100
counter
Radium
Prediction ( Base on Thomson's model )
1/
F+ ~ F-

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By C K Cheung
2/
F+ ~ F+’
F- ~ F-‘

Hence, no matter where the  particles hit, they should be deflected only by a small angle.
Experimental results:
..\powerpoint\atomic structure\Rutherford's expt..ppt
Thin gold
foil ~10 –7m
Pb
Radium
-
< 100
counter
very few
( 1 in 8000 )
1/
many ( > 99.5 % ) of the  particles go straight through the foil and were deflected through very
small angles ( < 100 ).
2/
very few ( ~ 1 in 8000 ) suffered deflections of more than 900.
Note:
1. gold is ductile
2. thin gold foil to avoid multiple collisions inside the foil.
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By C K Cheung
Rutherford’s model of atom
1/
Due to large-angle scattering of very few  particles  a small massive +ve core or nucleus.
2/
The –ve charge at relatively large distances from the nucleus so that their negative charge did not
act as a shield to the +ve nucleus charge when the  particles penetrate the atom.
3/
The –ve charge in circular motion to balance the electrostatic attraction.
Rutherford’s
model
of
atoms
(1911 )
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By C K Cheung
Rutherford’s estimate of nucleus size
r
b

u
v=0
Z
R
KEPE
..\powerpoint\atomic structure\size of atom.ppt
Z = atomic no.
= no. of proton inside nucleus
 KE = PE
1
1 (2e)( Ze)
 mu 2 
2
40
r
r=
Ze 2
0 mu 2
For closest approach: r = b
b=
Ze 2
0 mu 2
Take :
Z = 79
e = 1.6x10 – 19
0= 8.86x10 - 12
m=6.7x 10 – 27
u = 2x10 7 ms - 1
 b ~ 10 –14 m
R~
b
~ 10 – 15 m
2
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By C K Cheung
Limitations of Rutherford’s model
1/
By classical theories, all accelerating charged particles will emit radiation ( energy ).
If Rutherford’s model is correct, the accelerating electrons will lose energy continuously, then they will
be adhered to the nucleus and all atoms will finally be collapsed!
2/
Rutherford’s model does not predict the existence of discrete energy levels in atoms.
3/
Rutherford’s scattering experiment founded the high energy physics.
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By C K Cheung
Bohr’s Theory of atoms (1913)
Consider an H atom:
e
p
r

mv 2
(e)( e)
=
40 r 2
r
1
 v2 =
e2
40 mr
………………(1)
First Theory:
Only those orbits occur for which the angular momenta of the planetary electron are integral
h
h
multiples of
or n( )
2
2
h
 mvr = n(
)
2
h
 v = n(
)…………………(2)
2 mr
(2)  (1)
 n2h2 
e2
 2 2 2 =
40 mr
 4 m r 
 0h2 2
(n )
r=
me2


n2
r is in discrete values.
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By C K Cheung
For H-atom,
 r = 0.529( n2) x 10 – 10 m
If n = 1,  r1 = 0.529 A
If n = 2,  r2 = 2.11 A = 4 r1
Also, the energy of the system:
PE =
(e)( e)
40
r
KE =
1 2 1
e2
mv  m(
)
2
2 40 mr
1
Total energy = E = PE + KE = -

E=
-
me4
2
8 0 h 2 n 2
e2
80 r

-(
1
n2
)
e.g.
For max. E  n = _____________
For min. E  n = _____________
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By C K Cheung
Consider:
n5
E5
n4
E4
n3
E3
n2
E2
n1
E1
E12  - (
1
2

1
2
)= 3
4
2
1
5
E23 
36
 E12 > E23 > …………….
As n   E  0  continuous
Hence:
E
Formula:
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By C K Cheung
En = - 13.6 (
1
)
n2
eV
1 eV = ________________J
Second Theory
No electron radiates energy so long as it remains in one of the orbital energy states, and that radiation
occurs only when an electron goes from a higher energy state to a lower one, the energy of the quantum
of radiation = hf.
n2
E = En2 – En1 = hf
n1
c
me4
1
1
( 2  2 )  hf = h( )

2 2

8 0 h n1
n2
me4
1
1
 wave number  ( 2 3 )( 2  2 )


8 0 h c n1
n2
1
Rydberg constant R,
R=1.0973x107m-1
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By C K Cheung
e.g.
The diagram shown gives some levels of an atom. In the unexcited state the levels above
eV are unoccupied.
( Given: h = 6.6x10 - 34 Js, C = 3x108 ms-1, e = 1.6x10 -19C)
- 10.4
0 eV
- 1.6eV
- 3.7eV
energy in eV
- 5.5eV
- 10.4eV
a/
What is the ionization energy of the atom?
Ionization energy = 0 – (-10.4) = 10.4 eV
b/
What change is taking place if radiation of wavelength 141 nm is emitted?
Ans.: - 1.6eV to
- 10.4 eV
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By C K Cheung
e.g.
a/
Find the energy required to excite a hydrogen atom from the ground state to the
n = 4 state.
E = 13.6 (
1 1
 )eV
12 4 2
1
1
 2 ) x1.6 x10 19 C
2
1
4
-18
= 2.04x10 J
= 13.6 (
b/
How many different possibilities of spectral line emission are there for the atom when the electron
goes from n = 4 to the ground state ?
Note:
n=4
n=3
n=2
 possible number of spectral
lines = 6
n=1
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By C K Cheung
Evidence of energy levels
1/
Optical line spectra
(optical ~ visible region)
A particular line ( or a set of lines ) in an optical emission spectrum indicates the presence of a
particular frequency emitted in a transition of e ( directly or in stages ) between energy levels
2/
X-ray spectra
Photoelectric Effect
Source of variable
& known frequency
(f)
vacuum
A
Emitter
collector
V
Results of Experiment ( Laws of Photoelectric Emission )
1/ When the incident light is monochromatic, the number of photoelectrons emitted per
second
( current I ) is proportional to the light intensity ( I’). Such an emission
occurs effectively
instantaneously.
I/ A
V, f = constant
I’/Wm -2
Wave theory: the incident light energy is uniformly distributed amongst the free
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By C K Cheung
electrons in the emitter, we should predict time delays of ~ 103 seconds.
2/ The KE of the emitted electrons varies from 0 to a maximum value. This definite
depends only on the frequency of the light, and not on its intensity.
..\powerpoint\atomic structure\photoelectric effect1.ppt
maximum
I /A
f = constant
2I’
I’
V/V
Vs
0
Vs: stopping potential
1
2
mvmax  eVs
2
Wave theory: we feel hotter in sunlight than that in moonlight,  K.E. of the emitted
e should depend on light intensity.
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By C K Cheung
3/ Electrons are not emitted when the light has a frequency lower than a certain
The value of fo varies from metal to metal.
threshold value fo.
I/A
I’ = constant
A
fo
B
f/Hz
fo’
Wave theory: cannot predict the existence of
fo!
Explanation
Planck’s Theory (1900)
When radiation was emitted or absorbed, the emitting oscillator always showed
discrete sudden change of E, where E = hf.
a
Einstein’s Theory (1905)
Extended Planck’s original idea by suggesting that E.M. wave could exhibit
particle ( called photon ) behavior
1/ Electron emission is the result of a direct collision between an electron and a photon,
is no time delay before emission starts
..\powerpoint\atomic structure\photoelectric effect2.ppt
so there
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2/
By C K Cheung
Light intensity   number of photon arriving per m per second  but not energy of
individual photon .
2
I’ , f
2I’ , f
3/ fo depends on the material because each material requires a certain minimum energy
work function , W ) to free an electron.
( called
W = hfo
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By C K Cheung
Formula:
hf
1
mv 2
2
W
1
mv 2
2

hf = W +

hf = hfo +
1
mv 2
2

hf = hfo + eVs
This formula was verified by Millikan in 1916
Vs/V
slope =
fo’
h
e
f/Hz
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