sces1200 l03 electronic structure of atoms qm student03
TRANSCRIPT
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SpectroscopyBohr Atomic Structure
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From Classical Physics
Classical physics inability to explain atomic structure
Unable to explain emission spectra
Unable to explain blackbody radiation, photoelectric effect
Thomsons atomic model
If an electron (-ve) is stationary, it will be pulled towards the nucleus (+ve).
Rutherfords atomic model
If an electron is continuously orbiting the nucleus, it will emit light
(energy). Soon, electron will lose its energy; and will be pulled towards the
nucleus.
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Rydberg suggested a complete equation for the other lines outside
the visible light (infra red, ultra violet) region:
WHERE NINITIAL CAN TAKE VALUES OF N: 1, 2, 3, 4, . AND NFINAL : N+1, N+2, N+3 .
COMPLETE HYDROGEN LINE SPECTRUM
n1 n2 SERIES
12
3
4
5
2,3,4, .3,4,5, .
4,5,6, .
5,6,7, .
6,7, .
LymannBalmer
Paschen
Brackett
Pfund
http://en.wikipedia.org/wiki/Image:Rydberg-Physicist%25281854-1919%2529.jpghttp://en.wikipedia.org/wiki/Image:Rydberg-Physicist%25281854-1919%2529.jpg -
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Bohr
http://en.wikipedia.org/wiki/Image:Niels_Bohr.jpghttp://en.wikipedia.org/wiki/Image:Niels_Bohr.jpg -
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By combining CLASSICAL and QUANTUM theories and based on Plancks
hypothesis and information on atomic spectrum, Bohr postulated on the
hydrogen atom:
1. The electron moves in circular orbit around the nucleus.
2. The electron has only a fixed set of allowed orbits called stationary
states. The electron in the allowed orbits have unique values. As long as
an electron remains in a given orbit, its energy is constant and no energy
is emitted. Allowed values for the electron is called the angular
momentum are quantised in multiple values of h/2.
3. An electron can pass only from one allowed orbit to another. During such
transitions, fixed discrete quantities of energy (quanta) are involved
either absorbed or emitted.
Bohrs Postulate
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Bohr Atomic Model
Predict permissible radii of orbits for hydrogen atom rn = n
2a0
where n = 1, 2, 3, .
Bohr radius, a0 = 0.53 A (53 pm)
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Ionization of Hydrogen
Calculate the energy absorbed and released when excited or light
emission. The change in energy when electron changes orbit;
E is negative when energy/light is emitted
Calculate ionization energy
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Calculate ionisation energy
Explain the line spectrum of hydrogen according
to Planck equation
If,
Then,
Ionization of Hydrogen
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Inadequacies of Bohr Model
Only applicable to hydrogen and hydrogen-like ions (He+,
Li2+, Be3+ )
Unable to explain emission spectra of atoms and ions withmultielectrons
No fundamental basis for the postulate of quantized angular
momentum
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New Quantum Mechanics
Several failures in Bohr model
Need: quantisation of energy for system initially fulfilled by
Newtonian mechanics
Need: a new approach to resolve the wave-particle conflict
Need: to introduce the concept of quantisation of energy
using acceptable basis
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Einstein (1905) suggested that light has a particle-like properties
as embodied in photons (photoelectric effect).
In dispersion of light by prism..
Using the following:
(by Planck)
(by Einstein)
de Broglie (1924) apply the concept and suggested the wave-particle duality with the equation:
Wave-Particle Duality
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Every object in momentum (p) will possess a wavelength ()
ParticleMass
(kg)
velocity
(m s-1)
(10-12 m)
Electron (gas) 9 x 10-31 1 x 105 7000
He atom (gas) 7 x 10-27 1000 90
Base ball 0.1 20 3 x 10-22
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X-RAY DIFFRACTION
[WAVE]
ELECTRON DIFFRACTION
[PARTICLE]
Wavelengths for macroscopic particles are difficult to measure
too small
The wave property/nature of electron was proven in an
experiment involving diffraction of electron (1927)
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Heisenberg Uncertainty
Principle For a macroscopic particle (bullet, golf ball), its location and
speed can be determined simultaneously
For a microscopic and subatomic particle like electron, its
location and momentum cannot be determined with light;
because light are photons which will collide with the electron,
displacing its position and altering its momentum
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Uncertainty in position is:
Uncertainty in momentum is:
The resultant uncertainty in momentum and location is:
approximately:
or more specifically:
Heisenberg Uncertainty
Principle
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The Heisenberg Uncertainty Principle states that ...it is impossible to
know both the exact position and the exact velocity of an object at the
same time.
However, the effect is tiny and so is only noticeable on a subatomic scale.
Heisenberg Uncertainty
Principle