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?

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

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!

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

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!!!

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

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

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

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!

Electron Microscopes

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

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?

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!

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

Rutherford Scattering Instead, what was observed was alphas were scattered in all directions

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

Rutherford Scattering The model predicted how many alphas should be scattered at each possible angle Consider the impact parameter

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

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!!!

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!

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

Atomic Spectra Hydrogen spectrum has a pattern!

Atomic Spectra Balmer showed that the relationship is

Atomic Spectra Lyman Series Balmer Series Paschen Series

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

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!!!

Wave-Particle Duality