# Unit 7: Modern Physics

## Concepts

**Inertial reference frame** - Any reference frame which is at rest or moving at a constant velocity.

**Postulates of special relativity** - Two assumptions Einstein made when he developed his theory of special relativity. The first postulate states that the laws of physics are the same for any inertial reference frame. The second postulate states that light travels through empty space with a speed c independent of the speed of the source or observer.

**Mass-energy equivalence** - One of the main takeaways from the theory of special relativity, which is that mass and energy are related and can be interchanged.

**Wave-particle duality** - The concept that light can exist both as a wave and as particles.

**Photoelectric effect** - An effect that happens with certain metals when they absorb light of a certain frequency, which leads to electrons being emitted from the metal. This effect depends on the frequency of the light and the work function of the metal, NOT the intensity!

**Work function** - With the photoelectric effect, this is the work required to separate an electron from a metal.

**Atom decay** - When an atom loses particles and changes in some way, often by changing to a new element. The types of decay include:

- Alpha decay, where an atom emits an alpha particle upon decay. When alpha particles are emitted, it stabilizes the atom.
- Beta decay, where an atom emits both a beta particle and an antineutrino. With beta decay, the beta particle can be either an electron or a positron. Beta decay causes atoms to become unstable.

**Planck's constant** - 6.626 x 10^{-34} J⋅s.

**Speed of light** - 3 x 10^{8} m/s.

**Lorenz transformation** - 1/√(1-(v^{2}/c^{2})).

## Formulas

**△t=(△t _{o})/√(1-(v^{2}/c^{2})** - Formula used for time dilation. (Difference in time elapsed) = (time elapsed in inertial reference frame)(Lorenz transformation).

**E = mc ^{2}** - Einstein's famous equation, which says that mass and energy are interchangeable. Energy = (mass)(speed of light)

^{2}.

**E = hf** - Can be used to find the energy of a photon. (Energy) = (Planck's constant)(frequency of the photon).

**K _{max} = hf - φ** - Used when observing the photoelectric effect. (Kinetic energy of the electron ejected) = ((Planck's constant)(frequency of light being absorbed) - (work function of the metal).