Review of atomic model Davisson Geremer experiment

1. M
A
T
T
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R W
A
V
E
S Presented By,
Nagaveni G H

2. FAILURE OF
CLASSICAL
MECHANICS

3. CLASSICAL PHYSICS [ Pre
1900]
• Newtonian Mechanics
• Boltzmann, Gibbs…. Thermodynamics
• Maxwell…Electrodynamics
• Einstein’s General relativity and special relativity
• Classical chaos theory and nonlinear dynamics
• …………….

4. Classical mechanics is dominated by two
fundamental concepts.
Concept of a particle, a discrete entity with
definite position and momentum which moves in
accordance with Newton's laws of motion.
Concept of an electromagnetic wave, an
extended physical entity with a presence at
every point in space that is provided by electric
and magnetic fields which change in accordance
with Maxwell's laws of electromagnetism.

5. The classical world picture is neat and tidy: the laws of
particle motion account for the material world around
us and the laws of electromagnetic fields account for the
light waves which illuminate this world.
Scientists believed that:
The physical universe was deterministic.
Light consisted of waves, ordinary matter
was composed of particles.
Physical quantities (energy, momentum, etc.)
could be treated as continuous variables.
There exists an objective physical reality
independent of any observer.

6. We review some experimental evidences
showing that several concepts of classical
mechanics cannot be applied.
The black-body radiation
Atomic and molecular spectra
The particle-like character of EMR
The photoelectric effect

7. BIRTH OF

8. What happened to those ideas?
The development of quantum mechanics meant for those four
“certainties” of classical physics:
Classical : The physical universe is deterministic.
Quantum : The physical universe is not deterministic. At
the scale of atomic particles, the best that we can do is
find the probability of the outcome of an experiment.
We can’t predict exact results with certainty. Uncertainty
is an intrinsic property of matter at this level.
Classical : Light consists of waves, while ordinary matter
is composed of particles.
Quantum : Both light and matter exhibit behaviour that
seems characteristic of both particles and wave.
(wave-particle duality)

9. Classical : Physical quantities (energy, momentum, etc.)
can be treated as continuous variables.
Quantum : Under certain circumstances, some physical
quantities are quantized, meaning that they can take on
only certain discrete values.
Classical :There exists an objective physical reality
independent of any observer.
Quantum : It appears that the observer always affects the
experiment. It is impossible to disentangle the two.

10. REVOLUTION IN THE
ATOMIC MODEL

11. DALTON’S BILLIARD BALL MODEL
(1803)
Recommended atoms of a particular element differ from other
elements.+
Atoms aren’t indivisible.-

12. THOMSON’S PLUM PUDDING
MODEL [1904]
Recommended Electrons as components of atom.
No mention of nucleus.
+
-

13. RUTHERFORD’S NUCLEAR MODEL
[1911]
Recommended protons as components of atom; Mention of nucleus;
Realized positive charge was localized in the nucleus of an atom.
Do not explain why electrons remain in an orbit around the nucleus.
+
-

14. BOHR’S PLANETARY MODEL [1913-
1924]
Proposed stable electron orbits;
Explained the emission spectra of some elements.
Moving electron should emit energy and collapse into the nuclear model;
Do not work well for Heavier atoms.
+
-

15. At this point in 1924, Prince Louis De-Broglie
made the following observations -
The whole universe is composed of matter and electromagnetic
radiations. Since both are forms of energy so can be transformed
to each other.
The nature loves symmetry. As the radiation has dual nature,
matter should also posses dual character.

16. DE-BROGLIE ‘s MATTER WAVES
MODEL OF ATOM:
+
The waves associated with moving particle
are matter waves or De-Broglie waves.

17. QUANTUM MECHANICAL
(SCHRODINGER’S) MODEL OF ATOM
[1926-PRESENT]

19. M
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22. [1924]
=
𝒉
𝒎𝒄
=
𝒉
𝒎𝒗

23. De-Broglie wave velocity is given by,
𝑽 𝒑 =
𝒄 𝟐
𝒗
It is assumed that the De-Broglie wave group associated
with a moving particle travels with the same velocity as
that of particle.

24. WAVE PACKETS:
A Wave packet is a group of several waves of slightly
different velocity and different wavelength.

25. Phase velocity:
The velocity of component waves of a wave
velocity 𝒗 𝒑.
Group velocity:
The velocity with which the wave packet
superposition of waves travelling in a group

26. Group and Phase Velocity:

27. Consider two waves of same amplitude and of
slightly different frequencies and wavelengths
superpose and form wave packet.
𝝎 𝟏 = 𝟐𝝅𝒗 𝟏 𝝎 𝟐 = 𝟐𝝅𝒗 𝟐
𝒌 𝟏 =
𝟐𝝅
𝝀 𝟏
𝒌 𝟐 =
𝟐𝝅
𝝀 𝟐
These waves are represented as
𝒚 𝟏 = 𝒂 𝐬𝐢𝐧 𝝎 𝟏 𝒕 − 𝒌 𝟏 𝒙
𝒚 𝟐 = 𝒂 𝒔𝒊𝒏 𝝎 𝟐 𝒕 − 𝒌 𝟐 𝒙
The displacement equation of the wave packet
obtained due to their superposition will be
𝒚 = 𝒚 𝟏 + 𝒚 𝟐 = 𝟐𝒂 𝐜𝐨𝐬
∆𝝎
𝟐
𝒕 −
∆𝒌
𝟐
𝒙 𝐬𝐢𝐧 𝝎𝒕 − 𝒌𝒙

28. Since phase 𝝎𝒕 − 𝒌𝒙 = constant, then
For the amplitude of the wave packet,
∆𝝎
𝟐
𝒕 −
∆𝒌
𝟐
𝒙 = constant
Hence group velocity,
Phase velocity =
𝒅𝒙
𝒅𝒕
=
𝝎
𝒌
𝒗 𝒈 =
𝒅𝒙
𝒅𝒕
=
∆𝝎
∆𝒌

29. 𝒗 𝒈 = 𝐥𝐢𝐦
𝝎 𝟏→𝝎 𝟐
∆𝝎
∆𝒌
=
𝒅𝝎
𝒅𝒌
𝝎
𝒌
= 𝒗 𝒑 𝝎 = 𝒌𝒗 𝒑
𝒗 𝒈 =
𝒅
𝒅𝒌
𝒌𝒗 𝒑 = 𝒗 𝒑 +
𝟐𝝅
𝝀
𝒅𝒗 𝒑
𝒅 (
𝟐𝝅
𝝀
)
This is the required relation between group
velocity and phase velocity in dispersive medium.
𝒗 𝒈 = 𝒗 𝒑 − 𝝀
𝒅𝒗 𝒑
𝒅𝝀

30. In a non-dispersive medium,
𝒅𝒗 𝒑
𝒅𝝀
= 𝟎
𝒗 𝒈 = 𝒗 𝒑

31. The relationship between phase velocity, group
velocity and velocity of light is given by
𝒗 𝒈 𝒗 𝒑 = 𝒄 𝟐

32. EXPERIMENTAL EVIDENCE FOR
MATTER WAVES

35. Observations made for different accelerating voltages and a
number of curves are as shown in fig.

36. According to De-Broglie’s theory, the
wavelength of 54V electrons is given by
𝝀 =
𝒉
𝟐𝒎𝒆𝑽
=
𝟏𝟐.𝟐𝟓
𝑽
=
𝟏𝟐.𝟐𝟓
𝟓𝟒
= 𝟏. 𝟔𝟔 A˚
According to experiment, the diffracted
beam at 50˚ for Nickel crystal for [111]
reflecting plane d=2.15 A˚.
Applying the equation for a plane
reflection grating, 𝑑 sin 𝜃 = 𝑛λ
𝝀 = 𝟐. 𝟏𝟓 × 𝐬𝐢𝐧 50˚ = 𝟏. 𝟔𝟓 A˚
Experimental value is in good agreement with the theoretical value.
This shows that the beam of electrons behave like X-rays suffers
diffraction at reflecting surfaces and exhibits wave like properties.

37. Application of Matter Waves:
Because electrons behave as waves, they
can be used to “illuminate” objects in a
manner similar to light. An electron
microscope is an instrument that takes
advantage of this situation. In electron
microscopes, wavelengths as much as
100000 times smaller than those of visible
light can be achieved. With such small
wavelengths, electron microscopes can
reveal features that are as small as
0.000000001 meters (1 nm).