information about De broglis hypothesis 1

1. DE BROGLIS
HYPOTHESIS
CREATED BY -MR.ROHIT CHAUDHARI

2. Einstein’s postulate
A BEAM OF LIGHT CAN BE TREATED AS A STREAM OF PARTICLES (PHOTONS)
WITH ZERO REST MASS
EACH PHOTON HAS ENERGY:
WHERE H IS A CONSTANT (PLANCK’S CONSTANT, H ≈ 6.63 X 10-34 JS)
F, Λ, C, ARE FREQUENCY, WAVELENGTH AND VELOCITY OF LIGHT (IN VACUUM) RESPECTIVELY
LIGHT INTENSITY IS PROPORTIONAL TO PHOTON FLUX (NO OF PHOTONS PASSING THROUGH
UNIT AREA PER SECOND)

hc
hf
Ep 


3. So, an electromagnetic wave of wavelength λ and
frequency f can be thought of as a stream of
particles with energy E and momentum p given by:
Wave-particle Duality
hf
E


h
p 

4. The de Broglie Hypothesis
In 1924, de Broglie suggested that if waves of wavelength λ were
associated with particles of momentum p=h/λ, then it should also
work the other way round…….
A particle of mass m, moving with velocity v has momentum p given
by:

h
mv
p 


5. Kinetic Energy of particle
If the de Broglie hypothesis is correct, then a stream
of classical particles should show evidence of wave-
like characteristics.
m
k
m
h
m
p
KE
2
2
2
2
2
2
2
2






6. De Broglie wavelength of everyday
objects.
Eg. Tennis ball….
Mass ~60g
Velocity ~ 100mph ≈ 45 m/s
De Broglie wavelength = 10-33 M.

7. Observation of wave-like
behaviour
Just like a classical wave, effects such as diffraction and interference observed
when the wave interacts with objects with dimensions of the same order as the
wavelength, ie
So, wave-like properties not observed for everyday macroscopic objects, which
have de Broglie wavelengths ~10-34 m.
d
~


8. Electron Diffraction

9. Electron Diffraction

 sin
2
d
n


10. Standing de Broglie
Eg. electron in a “box” (infinite potential well)
V=0
V= V=
Standing wave formed
V=0
V= V=
Electron “rattles” to and fro

11. When do quantisation effects
become important?
Rule of thumb: at temperatures below which kT becomes comparable with ΔE.
For our confined electron (example 1), T~10000K
For our oxygen molecule, T~10-15K !!!!!!!!
So, quantisation effects easy to observe for electron, whereas the translational
motion of the gas atom in the “normal sized” box obeys classical mechanics
(continuous energy distribution)
(NB kT at room temperature (300K) is about 0.025eV)

12. The Bohr Model (1912-13)
Bohr suggested that the electrons in an atom orbit the positively-charged nucleus,
in a similar way to planets orbiting the Sun
(but centripetal force provided by electrostatic attraction rather that gravitation)
Hydrogen atom: single electron orbiting positive nucleus of charge +Ze, where Z
=1:
r
v
F
+Ze
-e

13. Failure of the Classical model
The orbiting electron is an accelerating charge.
Accelerating charges emit electromagnetic waves and therefore lose energy
Classical physics predicts electron should “spiral in” to the nucleus emitting continuous spectrum of
radiation as the atom “collapses”
CLASSICAL PHYSICS CAN’T GIVE US STABLE ATOMS………………..

14. Electron standing waves and the
Bohr Model
Bohr’s suggestion that orbital angular momentum of
electrons is quantised is equivalent to the requirement that
an integer number of de Broglie wavelengths must fit into
the electron orbit:

15. Electron standing waves and the
Bohr Model
n
r
n 
2
 n
n
e
r
v
m
h
n 
2

n
n
e
n r
v
m
L

n
e
n
n
e v
m
L
v
m
h
n

2


n
nh
L
n 


2

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