Unit 12 Quiz

Special relativity

Einstein’s scientific theory that explains how speed, time, and space interact

Reference frame vs inertial reference frame

A reference frame is simply any coordinate system used to observe and describe the position, motion, or physical state of a system. An inertial reference frame is a specific type of reference frame that has a constant velocity and therefore is not accelerating in any way (you can ignore acceleration if a question indicates that it turns really fast)

Inertial reference frame is the “special” part of special relativity

1st postulate of relativity

The laws of physics are the same in all inertial reference frames

(ie. all observers must agree on the equations used)

2nd postulate of relativity

The speed of light in a vacuum is constant from every observers POV, regardless of their relative motion

(Accepts null results of MM experiment and throws out aether theory by stating that light can travel through a vacuum and speed is constant”

Speed of light

3.0 × 10^8 m/s = c

Nothing can travel as fast/faster than speed of light

Every observer in the universe will agree on it

How does the relativistic train work (time dilation)

There are 2 observers, one stationary and one moving. Each observer will have an event clock. Identify the events (ie light ray sent, light ray received) and find the time between the two events. In the end, ∆t=∆t₀

Proper time equation & definition (∆t₀)

∆t₀=2d/c

Time measured by observer at rest with respect to the event clock

Ie the time interval between two events measured by an observer who is at rest relative to the events happening

Time dilation main equation

∆t = ∆t₀ / √(1-(v²/c²))

Special relativity equation & meaning

y = 1 / √(1-(v²/c²))

Lorentz Faction (gamma, y)

Only exists when the velocity is much smaller than c

When v <<c, then y is approximately 1, meaning you dont notice it

You would need an infintate amount of energy for v to equal c

Time dilation equation and definition

∆t=∆t₀/√(1-(v²/c²))

At small speeds, ∆t=∆t₀

At speeds comparable to light, ∆t > ∆t₀

*Moving Clocks tick slower* —> the individual observer does not notice anything different about time, only when you compare clocks in different reference frames will you find they disagree on how time flows

Twin paradox steps

Determine the following

1. What are the two events we should measure the time between

2. Who measures the proper time, t∆₀ (who is at rest w/ both objects

Earth twin age difference, rocket twin only ages amount of time that rocket is gone

Time dilation simple equation

∆t=y∆t₀

Where proper time is the shortest time between any two events

Lightyear

unit of distance

v=d/t, c=d/t, ct=d - light(unit of time)

Length Contraction equation and explaination

L = √(1-v²/c²) (L₀)

L=L₀/y

The stationary observer is at rest with length L, which they call L₀.

Moving lengths are shorter, and only the lengths parallel to the direction of the motion contract

Proper length is the longest distance between any two locations

Proper length

L₀=v∆t

The length measured by an observer at rest w.r.t. two points

Observers agree on relative speeds

Simultaniety

events that are simultaneous in one reference frame are not simultaneous in another. An obersever outside of the train will measure that the detectors do off at different times. Both persepctives here are correct

Relativistic Mass equation and definition

m=m₀/√(1-v²/c²)

m = ym₀

moving masses are larger bc as your relative motion increases, so does your inertia, making it more and more difficult to increase your motion as you go

Mass-Energy Equivalence

E=mc² = rest energy

E=m₀/√(1-v²/c²)

an object has an intrinstic amount of energy simply bc it has mass

Main idea of quantum mechanics

Particles often exhibit wave properties

Waves frequently behave like particles

Main different between particles and waves

Particles: Determinism —> certain location

Waves: Probabilistic —> spread out

Attributes of waves vs particles

Waves: wavelength, frequency, carry energy, interference

Particles: mass, transfer energy, momentum, no interference (Pauli Exclusion principle)

Pauli exclusion principle

No objects can have the same state at exactly the same time

Ex: electrons, spin up/down, only one of each allowed in each orbital shell

Properties associated with particles, not waves

Double-Slit Experiment

Evidence of lights behavior as a wave

Diffraction & interference are processes associated with waves, not particles

Newtons Cradle shows…

Particles never overlap or interfere

Compton’s Experiment

The material absorbes some energy, light acts as a particle, transfering momentum to the electrons on the surface. effect is called Compton Scattering

Photoelectric effect

Shows that waves (light) can behave like particles using anode and cathode

Initially, there is no current (I=0), but when radiation (light) falls on a piece of metal, photo-electrons are emitted (electrons that are ejected by light)

Anode vs Cathode

Anode: positively charged material (accepts anions, negative charges, larger line)

Cathode: negatively charged material (accepts cations, positive charges, shorter line)

When does photoelectric effect happen

Only happens if the frequency of radiation is above the minimum value threshold frequency f₀, which depends on the CATHODE material

Not all light rays have enough energy to eject an electron

Photoelectric effect in depth explanation

Light incident on clean metal surface can cause electrons to be ejected from the surface. Time between the introduction of light and the ejection of the electron is short, so it must be the light ejective the electrons. Whether or not electrons are actually ejected from the metal depends on the frequency of the light. Above a certain frequency, an electron is ejected and below, no electron is ejected. If electrons are ejected, a higher frequency of light causes the electron to have more KE, therefore higher speeds and more current in the circuit.

Quantization of energy

energy comes in bundles or packets of energy, called photos

relationship between energy of light and frequency

proportional

Energy of photon equation

Ephoton = hf

where h is plancks constant

planck’s constant

h = 6.63 × 10^-34 J/Hz

Conservation of energy equation

Ephoton = W₀ + KE

where W₀ = hf₀ (f₀ is the threshold frequency, or the minimum frequency needed to eject an electron)

W₀ = Work Function = amount of work done (energy added)

KE equation

KE of electron = hf - hf₀

Unit: electronvolt: 1eV = 1.6 × 10^-19 J

KE = ½ mv²

KE/v = ½ mv

Relation with energy and speed to momentum

Energy/speed is proportional to momentum

Momentum equation

p = h/λ

Compton Effect

Energy and momentum gained by electron = energy + momentum lost by the photons

Light waves have momentum, but no mass

deBroglie Hypothesis concept and equation

All moving matter has a wavelength associate with it, just as a wave does

λ = h/mv

All objects, no matter how hot or cold, continuously radiate electromagnetic waves

double split experiment

When observing: e acts like a particle

When not observing: e acts like a wave

you get different answers depending on whether you interact/observe the electron or not

Creates the observer problem with different explanations

schrodinger’s Cat

Implies that the cat is both alive and dead at the same time until observed and one state is confirmed. Main idea: the electron is only definitively at a location when/if you measure it, otherwise its location is not definitive, but spread out (everywhere literally)

Heisenberg Uncertainty principle

the position and momentum of a particle cannot both be precisely known at the same time

∆x ∆p ≥ h/4π

Not experimental error

Atom

In a nuetral atom #p+ = #n⁰

Mass of p+ = n⁰

Top number is the mass number (protons + nuetrons)

Bottom number is the number of protons (and also number of electrons)

Isotopes

atoms of the same element that have different amounts of nuetrons. Written as element + mass number(top number)

Ionization

the process of adding or removing electrons from a neutral molecule, making it charged

radioactive decay definition

some nuclei are unstable and disintegrate sponstaneously emitting energetic particles and/or photons/ligjt

strong nuclear force

force that bonds the nucleus of an atom. this force also is responsible for binding quarks together (quarks are fundamental particles that make up protons and nuetrons)

Alpha Decay

α= 4/2 HE

Tunnels our of nucleas, suddenly appearing outside

Type of strong nuclear force

Weak nuclear force

allows particles to charge tupe, causing transmutation (conversion) of one particel to another. ie Protons to nuetrons and vice versa

Probability of the sudden change of one type of particle to another. Resutls in different types of anti-matter (regular matter but opposite charge)

Beta minus decay

0/-1 e

nuetron decays into proton and electron

beta plus decay

0/+1 e

proton decays into nuetron and positron

gamma decay

just plus +γ , there is no change, just releasing energy

0/0γ

Half life

the most likely length time required for which you would expect half the atoms in any given quanity of a radioactive isotope to decay

Nremaining = N₀ (1/2)^n