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Rutherford’s Model of the Atom

• Most of the atom is empty space.

• Most of the atom’s mass and + charge is located at the center of the atom.

Next

• Bohr’s model

• How a laser works

• X-ray production

• Wave-particle duality

• Quantum Physics

Exercise

• A radiostation broadcasts at 89.3 MHz with a radiated power of 43.0 kW.

a) What is the magnitude of the momentum of each photon?

b) How many photons does the radiostation emit each second?

Exercise

For a certain cathode material in a photoelectric-effect experiment you measure a stopping potential of 1.0V for light for wavelength 600nm, 2.0 V for 400 nm, and 300nm for 300nm. Determine the work function for this material and the value of Planck’s constant.

Emission spectral

Things to consider

1. Unique spectral lines for each element.

2. Each spectral line has a particular frequency => particular photon energy

3. Heavy positively charge nucleus in the center of the atom arounded by electrons.

• Attraction between negative electrons and positived nucleus.

• Rutherford’s proposal

+

- -

--

-

Bohr’s model

• Electrons move around the nucleus at stable orbits without emitting radiation.

• Electron in one of these stable orbit has a definite energy.

• Energy is radiated only when electrons make transitions from high energy orbit to a low energy orbit.

• Energy is emitted as photons with energy

initial finalhf E E

+

--

Quantifying the energy spectrum

• Bohr postulate that the angular momentum of an electron revolving around a nucleus is quantized in units of h/2

n e n n

hL m v r n

2

• Newton’s 2nd law yields

2 2n

e20 n n

1 e vF m

4 r r

2 2

n 0 2e

n hr

m e

2

n0

1 ev

2nh

• The smallest radius is obtained by setting n = 1, is called the bohr radius.

2

0 0 2e

ha

m e

2n 0r n a

• Kinetic energy of moving electrons

n

2n e

1K m v

2

2

n0

1 ev

2nh

0

4e

2 2 2

m e18n h

• Potential energy of electron bound to + nucleus

2

n0 n

1 eU

4 r

2 2

n 0 2e

n hr

m e

4e2 2

0

m e14n h

Total energy of electron n-th orbital

n n n

4e2 2

0

E K U

m e18n h

Energy level diagram

• The possible energies which electrons in the atom can have is depicted in an energy level diagram.

1E

2E

3E4E

• In 1958, Charles Townes and Arthur Schawlow theorized about a visible laser, an invention that would use infrared and/or visible spectrum light.

• Light Amplification by Stimulated Emission of Radiation- (LASER).

• Properties of Lasers– Produce monochromatic light of extremely high

intensity.

Bohr’s model and the operation of the Laser

Bohr’s model and the operation of the Laser

Bohr’s model and the operation of the Laser

1E

2E

3E4E

Bohr’s model and the operation of the Laser

Bohr’s model and the operation of the Laser

1E

2E

3E4E

Bohr’s model and the operation of the Laser

1E

2E

3E4E

Bohr’s model and the operation of the Laser

Bohr’s model and the operation of the Laser

1E

2E

3E4E

Bohr’s model and the operation of the Laser

1E

2E

3E4E

Bohr’s model and the operation of the Laser

Bohr’s model and the operation of the Laser

X-ray production

• Properties of x-rays.– High penetration => High energy =>High

frequency.

• X-rays are produced when acelerated electrons strike a heavy metalic target (W).

Operation of an X-ray machine

X-ray production on the atomic scale

X-ray production on the atomic scale

ALLAN MACLEOD CORMACK : 1924-1998

• Lecturer in Physics, University of Cape Town, 1950 - 1957

• Nobel Prize for Physiology and Medicine, 1979

• Development of the CAT scanner (Computer Aided Tomography).

SIR AARON KLUG

• MSc student in Physics, University of Cape Town, 1946? - 1948

• Nobel Prize for Chemistry 1982

• Probing the properties of macromolecules (DNA) with x-rays.

Wave-Particle Duality

• In the Bohr model, electrons orbit the atomic nucleus in stable orbits.

• What makes an orbit stable?

• Louis de Broglie proposed that subatomic particles, such as electron, could exhibit some wave behaviour.

De Broglie’s Wave Particle Model

• Similar to photons

photonphoton

hp

• Wavelength of particle is related to its momentum by

partic lepartic le

hp

where

partic le

hmv

Bohr’s model with wavy electrons

• An electron orbit is stable if an integer number of de Broglie standing wave can fit into it.

+r

2 r

• General

n2 r n

• Yields

n n n nn

h hL p r r n

2

partic lepartic le

hp

Wave Phenomenon

• Phenomenon associated with waves include:

1. Interference effects

2. Reflection

3. Refraction

Interference

• Superposition of wave pulse

Davidson-Germer experiment

• Aim: to test if particle (electrons) exhibit properties of waves i.e. Inteference.

• Young’s experiment to find interference pattern due to particle wave interaction.

Electron diffraction pattern

Scanning electron microscope images

Theory of Quantum mechanics

• Understanding the nature of the particle waves.

• Heisenbergs uncertainty principle

• Schroedinger’s equation.

• Spin-off of quantum theory in the today’s world

Quantum Scale

Heisenbergs Uncertainty Principle

• On the scale on life size object a system is not influenced by measurements on a system (Deterministic system).

• On the atomic scale a measurement on a system will influence on it.

Finding the location of an electron

-

hp

ep m v

Finding the location of an electron

-

The Uncertainty Principle

• Act of measurement influences the electron’s state– Neither the position nor the momentum of a

particle can be determined with arbitrary great precision

x

hx p

2

Schroedinger’s Wave Equation

x

hx p

2

• Heisenberg Uncertainty + de Broglie waves = Schroedinger’s probabily waves function

2 2

2

d (x)V(x) (x) E (x)

2m dx

(x) A(cos kx i sinkx)

(x) Probability of finding a partic le at location x

Schroedinger’s solution to the electron orbitals in the

atom