Photoelectric Effect

• Ultraviolet light could cause some metals to spark (electrons to be emitted from the metal)
• Raising intensity of light (amplitude of light wave) could not cause electrons to be emitted if the frequency is not above a certain threshold (threshold frequency)
• Kinetic energy of emitted electrons increase as the frequency of the light increases

Einstein Photoelectric Equation

• Light consists of discrete or quantized packets of energy called “photons”
• KE_max = hf - hf₀, where KE_max is maximum kinetic energy of emitted electrons, h is planck’s constant, and f₀ is threshold frequency, and f is frequency of light
• hf₀ is the work function
• hf is energy of a photon E_photon = hf

Work function

The minimum energy needed to remove an electron bound to a metal surface. Work function Φ = hf₀

Experiments with various metals

Experiments with different metals show that though different metals have different threshold frequencies and therefore different work functions, they all obey the same photoelectric equation and have the same slope h.

Photon Energy, Mass, and Momentum

• Photon energy E_photon = hf
• Photon momentum P_photon = E_photon /c, which means P_photon = h / λ (λ is wavelength) 
• Photon does not have rest mass, ie, its m ≈ 0

We can prove why P_photon = E_photon /c:

Total energy E_total

Relativistic momentum p

For photon, v = c, so P_photon = E/c

Photon Interactions

When a photon comes into contact with matter, the interaction obeys law of conservation of momentum, and has 5 different results:

• A photon may simply reflect, as when potons of visible light undergo perfectly elastic collisions with a mirror
• A photon may free an electron and be asborbed in the process, as in the phtoelectric effect
• A photon may emerge with less energy and momentum after freeing an electron. After this interaction, the photon still travels at the speed of light but with less energy and a lower frequency. THis is the Compton effect.
• A photon may be absorbed by an indivudual atom and elevate an electron to a hgher energy level within the atom.
• A photon may undergo pair creation, where it becomes onverted into 2 particles with mass. This process conserves energy and momentum because all the energy of the photon becomes converted into the kinetic energy o fthe new particles and their rest mass energy.

Compton Effect

When a photon comes into contact with matter, the interaction may cause a photon to emerge with less energy and momentum after freeing an electron. After this interaction, the photon still travels at the speed of light but with less energy and a lower frequency. In the photoelectric experiment, it is observed that scattered photon has lower frequency and therefore lower energy.

Double-slit experiment

When you do double-slit experiment with particles such as tennis balls, they do not show interference effects.

When you do double-slit experiment with light, you see constructive and destructive interference produces bright and dark fringes on the screen.

When you do double-slit experiment with electrons, you see they produce the same constructive and destructive interference pattern on the screen as light.

Wave-Particle Duality

The double-slit experiment with quantum objects such as electrons and electromagnetic radiation such as light suggest that they have both wave-like and particle-like behavior - wave-particle duality:

• All quantum objects and electromagnetic radiation can exhibit interference (a wave property)
• All quantum objects and electromagnetic radiation transfer energy in distinct, or discrete, amounts (a particle property). These discrete "parcels" of energy are called quanta.

Matter waves

From the photon momentum equation P_photon = h / λ (h is planck’s constant and λ is wavelength), we have

λ = h / P_photon

To extend above to all classical particles, we have

λ = h / P = h / mv

The wavelength above that is associated with the motion of a particle (photon, electron, etc.) with momentum p is called the de Broglie wavelength. If a particle has a wavelength, the particle should exhibit interference as waves do. When particles are large, wavelength will be so small you will not see the wave; when particles are small at atomic level, you see wave like properties as in light and electrons.

Heisenberg Uncertainty Principle 

Heisenberg Uncertainty Principle says that there is a limit to how accurately simultaneous measurements of the position and momentum o f a quantum object can be. This is expressed as a mathematical statement that says that if Δx is the uncertainty in a particle's position, and Δp is the uncertainty in its momentum, then

ΔxΔp >= h / (4π), where h is planck’s constant.

Heisenberg Uncertainty Principle can be used to explain the double slit experiment of electrons. When an electron passes through a wide slit (large position uncertainty), the diffraction spot on the screen is narrow (small momentum uncertainty). When the slit is narrower (smaller position uncertainty), the diffraction spot becomes wider (larger momentum uncertainty).

Black body radiation

What is a black body? Black body is a kind of objects that do not reflect light. Black body objects absorb all incident light. There is no perfect black body in the world, but examples of objects that are close to black body are the sun, your black T-shirt, a pizza oven burning charcoal, etc.

When will a black body radiate electromagnetic waves? When its inside temperature heats up.

Wien’ law

According to Wien's law, as temperature heats up, an ideal blackbody will emit electromagnetic waves at different wavelengths. And as blackbody temperature increases, the wavelength at whcih the radiation intensity is largest, λ_max, will become shorter and shorter, given by the equation below (another way to summarize Wien's law is: peak wavelength is inversely proportional to temperature):

λ_max = (2.90 x 10^-3 mK) / T, where T is blackbody temperature in Kelvin, and 2.90 x 10^-3 mK is Wien's displacement constant (in meter kelvin).

Ultraviolet Catastrophe

The Wien's law predicts that as temperature increases, peak wavelength will keep shifting to the left. However, this is not what the experiment has found out. The blackbody experiment has shown that the intensity would dip down to the left of the UV portion of the spectrum, as temperature increases. (for more detailed explanation, refer to https://www.youtube.com/watch?v=7BXvc9W97iU)

Planck's Math Formula

The spectral radiance of a body, Bν, describes the amount of energy it gives off as radiation of different frequencies. It is measured in terms of the power emitted per unit area of the body, per unit solid angle that the radiation is measured over, per unit frequency. Planck showed that the spectral radiance of a body for frequency ν at absolute temperature T is given by

The above formula can fit the blackbody experiment results very well. But what is more important about Planck's blackbody formula for Quantum Physics is that in order to use the formula, you need to accept Planck's hypothesis that 

• Energy in a blackbody comes in discrete parcels (quanta).
• Each parcel has energy equal to hf, where f is frequency, and h is Planck's constant, with a value of 6.626 x 10 ^-34

For more detailed explanation, you can refer to https://m.youtube.com/watch?v=7hxYGaegxAM