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Physics

Light Quanta

Quantum Theory

Is light a WAVE or a PARTICLE?

▪ Particle – tiny object like a bullet, has mass and travels in straight lines unless a force acts upon it

▪ Waves – phenomena that extend in space, characterized by diffraction and interference

Evidence for Wave Nature

Thomas Young’s double slit experiment showed interference patterns, demonstrating light’s wave-like properties.

Maxwell reinforced Young’s results by predicting that light carries energy in oscillating electric and magnetic fields –waves.

Evidence for Wave Nature

Black Body Radiation & The UV Catastrophe

According to classical wave theory, the intensity should increase as the fourth power of the wavelength decreased.

At low wavelengths, then intensity should become infinite!

Wave theory could not explain the peak in the intensity.

Planck’s Constant and Photons

In 1900, Maxwell Planck hypothesized that radiant energy was emitted in discrete bundles or quanta, the energy of which is proportional to the frequency of radiation.

E ~ f

Microwave radiation can’t do the damage to molecules in living cells that UV light and X-Rays can.

EM radiation interacts with matter only in discrete bundles of photons. So the relatively low frequency of microwaves ensures low energy per photon.

Energy is Proportional to Frequency

UV light can deliver about a million times more energy to a molecule because its frequency is a million times greater than the frequency of microwaves.

Energy is Proportional to Frequency

Photoelectric Effect

Albert EinsteinRobert Millikan

The Photoelectric Effect

Evidence for Particle Nature

Ionization Energy

Ionization Energy, also called the work function, ф , is the minimum energy required to eject electrons from the atom and is equal to the absolute value of the ground state energy.

𝐾𝑚𝑎𝑥 = ℎ𝑓 − 𝜙

𝐾𝑚𝑎𝑥 = 𝐸𝑝ℎ𝑜𝑡𝑜𝑛 − 𝜙

1. Photons with very low frequencies create no potential in the photocell.

2. As the frequency of the photons is steadily increased, athreshold frequency was encountered that induced apotential in the photocell.

3. Increasing the intensity of the light (but using the samefrequency) increases the rate at which electrons are ejected, but they still have the same energy (Kmax). The voltage doesn’t change.

4. Increasing the frequency of the photons above thethreshold frequency increased the potential of thephotocell and the energy of the emitted electrons.


Kmax vs. Frequency

Wave-Particle Duality

𝑬 = 𝒉𝒇

Light is emitted / absorbed like a particle, but travels as a wave.

Double-Slit Experiment


Suppose we dim our light source, allowing onlyone photonat a time topass through and reach the film.

Light strikes as a particle,but

Light travels as a wave!

LIGHT ELECTRONS

Particles as Waves

Louis de Broglie

Every particle of matter is somehow endowed with a wave to guide it as it travels!

Yes, you read that correctly… electrons, protons, atoms, a mouse, you, a planet, a star…

They all have a wavelength that is related to it’s momentum.

Particles as Waves

Louis de Broglie

𝜆 =ℎ

𝑚𝑜𝑚𝑒𝑛𝑡𝑢𝑚

𝜆 =ℎ

𝑚𝑣

Particles as Waves

Problems

Calculate the wavelength of a bullet of mass 0.02 kg, traveling at 330 m/s.

Problems

Calculate the wavelength of an electron (mass 9.1 x 10-31 kg), traveling at 2% the speed of light.

Quantum Uncertainty

Uncertainty is related to the limits of our ability to make measurements and the idea that the act of measuring

something affects the quantity being measured.

“The theory says a lot, but does not really bring us any closer to the secret of the ‘old one’. I, at any rate, am convinced that He does not throw dice.”

- Albert Einstein

Quantum Uncertainty

Quantum Uncertainty

Observing vs. Probing

Quantum uncertainties are significant only in the atomic and subatomic realm.

Let’s measure the

speed of a pitched

baseball using a pair of

photogates that are a

know distance apart.

Quantum Uncertainty

Now, let’s use the

same apparatus to

measure the speed of

an electron.

Quantum Uncertainty

Quantum Uncertainty

Werner Heisenberg

The Heisenberg Uncertainty Principle states that it is not possible to measure exactly both the position and the momentum of a particle at the same time.

The Uncertainty Principle

Δ𝑝 Δ𝑥 ≥ ℏ

• If we wish to know the momentum of an electron with great accuracy (small delta p), the corresponding uncertainty in positionwill be large.

• If we wish to know the position of an

electron with great accuracy, (small delta x),

the corresponding uncertainty in momentum

will be large.

The Uncertainty Principle

Complementarity

Complementarity is the principle stating that the wave and particle aspects of both matter and radiation are necessary, complementary parts of the whole.

Niels Bohr

Other Interesting Quantum Phenomena

▪ Quantum Tunneling

▪ Entanglement (Spooky Action at a Distance)

▪ Quantum Computers

Physics

The Atom & The Quantum

Electron Waves

The idea that electrons can occupy only certain levels was first suggested by NeilsBohr in 1913.

Niels Bohr

Electron Waves

Why did electrons only occupy specific discrete energy states?It seems like an electron should be able to orbit at any distancedepending only on it’s speed, like any satellite.

Electron Waves

According to Classical Mechanics, an electron moving in a circular path should continually radiate energy and this loss of energy should cause it to spiral into the nucleus.

But this does not happen!

Electron Waves

Why the electron occupies only discrete levels is understood by considering the electron to be not a particle but a WAVE.

𝜆 =ℎ

𝑚𝑣

Electron Waves

An orbiting electron forms a standing wave only when the circumference of its obit is equal to a whole-number multiple of the wavelength.

Electron Waves

Cloud Model of the Atom

In the still more modern wave model of the atom, electrons move not only around the nucleus but also in and out, toward and away from the nucleus.

Erwin Schrödinger

Schrödinger’s Wave Equation

Richard Feynman

Quantum Mechanics

Correspondence Principle

▪ The correspondence principle says that in order for a new theory to be valid, it must account for the verified results of the old theory.

▪ When the techniques of quantum theory are applied in classical situations, the results are identical.

Other QM Topics to Investigate

▪ Quantum Entanglement

▪ Quantum Tunneling

▪ String Theory

▪ Superposition

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