SCES1200 L03 Electronic Structure of Atoms QM Student03

8/14/2019 SCES1200 L03 Electronic Structure of Atoms QM Student03

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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.


3/18

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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11/18

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


12/18

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


13/18

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


15/18

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)


16/18

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:


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.


Principle

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SCES1200 L03 Electronic Structure of Atoms QM Student03