wave-particle duality

26
Wave-Particle Duality • Last time we discussed several situations in which we had to conclude that light behaves as a particle called a photon with energy equal to hf • Earlier, we discussed interference and diffraction which could only be explained by concluding that light is a wave • Which conclusion is correct?

Upload: raina

Post on 21-Mar-2016

81 views

Category:

Documents


5 download

DESCRIPTION

Wave-Particle Duality. Last time we discussed several situations in which we had to conclude that light behaves as a particle called a photon with energy equal to hf Earlier, we discussed interference and diffraction which could only be explained by concluding that light is a wave - PowerPoint PPT Presentation

TRANSCRIPT

Page 1: Wave-Particle Duality

Wave-Particle Duality

• Last time we discussed several situations in which we had to conclude that light behaves as a particle called a photon with energy equal to hf

• Earlier, we discussed interference and diffraction which could only be explained by concluding that light is a wave

• Which conclusion is correct?

Page 2: Wave-Particle Duality

Wave-Particle Duality

• The answer is that both are correct!!• How can this be???• In order for our minds to grasp concepts we build

models• These models are necessarily based on things we

observe in the macroscopic world• When we deal with light, we are moving into the

microscopic world and talking about electrons and atoms and molecules

Page 3: Wave-Particle Duality

Wave-Particle Duality

• There is no good reason to expect that what we observe in the microscopic world will exactly correspond with the macroscopic world

• We must embrace Niels Bohr’s Principle of Complementarity which says we must use either the wave or particle approach to understand a phenomenon, but not both!

Page 4: Wave-Particle Duality

Wave-Particle Duality

• Bohr says the two approaches complement each other and both are necessary for a full understanding

• The notion of saying that the energy of a particle of light is hf is itself an expression of complementarity since it links a property of a particle to a wave property

Page 5: Wave-Particle Duality

Wave -Particle Duality

• Why must we restrict this principle to light alone?

• Might microscopic particles like electrons or protons or neutrons exhibit wave properties as well as particle properties?

• The answer is a resounding YES!!!

Page 6: Wave-Particle Duality

Wave Nature of Matter

• Louis de Broglie proposed that particles could also have wave properties and just as light had a momentum related to wavelength, so particles should exhibit a wavelength related to momentum

λ = hmv

Page 7: Wave-Particle Duality

Wave Nature of Matter

• For macroscopic objects, the wavelengths are terrifically short

• Since we only see wave behavior when the wavelengths correspond to the size of structures (like slits) we can’t build structures small enough to detect the wavelengths of macroscopic objects

Page 8: Wave-Particle Duality

Wave Nature of Matter

• Electrons have wavelengths comparable to atomic spacings in molecules when their energies are several electron-volts (eV)

• Shoot electrons at metal foils and amazing diffraction patterns appear which confirm de Broglie’s hypothesis

Page 9: Wave-Particle Duality

Wave Nature of Matter

• So, what is an electron? Particle? Wave?• The answer is BOTH• Just as with light, for some situations we need to

consider the particle properties of electrons and for others we need to consider the wave properties

• The two aspects are complementary• An electron is neither a particle nor a wave, it just

is!

Page 10: Wave-Particle Duality

Electron Microscopes

Page 11: Wave-Particle Duality

Models of the Atom

• It is clear that electrons are components of atoms

• That must mean there is some positive charge somewhere inside the atom so that atoms remain neutral

• The earliest model was called the “plum pudding” model

Page 12: Wave-Particle Duality

Plum Pudding Model

We have a blob of positive charge and the electrons are embedded in the blob like currants in a plum pudding.

However, people thought that the electrons couldn’t just sit still inside the blob. Electrostatic forces would cause accelerations. How could it work?

Page 13: Wave-Particle Duality

Rutherford Scattering

• Ernest Rutherford undertook experiments to find out what atoms must be like

• He wanted to slam some particle into an atom to see how it reacted

• You can determine the size and shape of an object by throwing ping-pong balls at the object and watching how they bounce off

• Is the object flat or round? You can tell!

Page 14: Wave-Particle Duality

Rutherford Scattering

• Rutherford used alpha particles which are the nuclei of helium atoms and are emitted from some radioactive materials

• He shot alphas into gold foils and observed the alphas as they bounced off

• If the plum pudding model was correct, you would expect to see a series of slight deviations as the alphas slipped through the positive pudding

Page 15: Wave-Particle Duality

Rutherford Scattering

• Instead, what was observed was alphas were scattered in all directions

Page 16: Wave-Particle Duality

Rutherford Scattering

• In fact, some alphas scattered through very large angles, coming right back at the source!!!

• He concluded that there had to be a small massive nucleus from which the alphas bounced off

• He did a simple collision model conserving energy and momentum

Page 17: Wave-Particle Duality

Rutherford Scattering

• The model predicted how many alphas should be scattered at each possible angle

• Consider the impact parameter

Page 18: Wave-Particle Duality

Rutherford Scattering

• Rutherford’s model allowed calculating the radius of the seat of positive charge in order to produce the observed angular distribution of rebounding alpha particles

• Remarkably, the size of the seat of positive charge turned out to be about 10-15 meters

• Atomic spacings were about 10-10 meters in solids, so atoms are mostly empty space

Page 19: Wave-Particle Duality

Rutherford Scattering

From the edge of the atom, the nucleus appears to be 1 meter across from a distance of 105 meters or 10 km.

Translating sizes a bit, the nucleus appears as an orange viewed from a distance of just over three miles!!!

This is TINY!!!

Page 20: Wave-Particle Duality

Rutherford Scattering

Rutherford assumed the electrons must be in some kind of orbits around the nucleus that extended out to the size of the atom.

Major problem is that electrons would be undergoing centripetal acceleration and should emit EM waves, lose energy and spiral into the nucleus!

Not very satisfactory situation!

Page 21: Wave-Particle Duality

Light from Atoms

• Atoms don’t routinely emit continuous spectra

• Their spectra consists of a series of discrete wavelengths or frequencies

• Set up atoms in a discharge tube and make the atoms glow

• Different atoms glow with different colors

Page 22: Wave-Particle Duality

Atomic Spectra

• Hydrogen spectrum has a pattern!

Page 23: Wave-Particle Duality

Atomic Spectra

• Balmer showed that the relationship is

=R 122 −1

n2⎛ ⎝ ⎜

⎞ ⎠ ⎟ for n=3,4,5,...

Page 24: Wave-Particle Duality

Atomic Spectra

• Lyman Series• Balmer Series• Paschen Series

=R 122 −1

n2⎛ ⎝ ⎜

⎞ ⎠ ⎟ for n=3,4,5,...

=R 112 − 1

n2⎛ ⎝ ⎜

⎞ ⎠ ⎟ for n=2,3,4,...

=R 132 −1

n2⎛ ⎝ ⎜

⎞ ⎠ ⎟ for n=4,5,6,...

Page 25: Wave-Particle Duality

Atomic Spectra

• Lyman Series• Balmer Series• Paschen Series• So what is going on here???• This regularity must have some

fundamental explanation• Reminiscent of notes on a guitar string

=R 122 −1

n2⎛ ⎝ ⎜

⎞ ⎠ ⎟ for n=3,4,5,...

=R 112 − 1

n2⎛ ⎝ ⎜

⎞ ⎠ ⎟ for n=2,3,4,...

=R 132 −1

n2⎛ ⎝ ⎜

⎞ ⎠ ⎟ for n=4,5,6,...

Page 26: Wave-Particle Duality

Atomic Spectra

• Electrons can behave as waves• Rutherford scattering shows tiny nucleus• Planetary model cannot be stable classically• What produces the spectral lines of isolated

atoms?• Why the regularity of hydrogen spectra?• The answers will be revealed next time!!!