problem set

mass

directly proportional to inertia and gravity

heat

experiment, found that __ does not have mass

Drill a hole into an iron bar → heat is released, but the iron bar and shreds of it that were drilled off have the same total mass as they did before

kinetic energy

 energy being exercised via movement

• Equally distributed among the allowable types of motion, so based on the temperature, you know what’s going on on a smaller level

potential energy

energy that may be exercised in the future because an object with potential energy has forces acting on it

thermal energy/heat energy

energy released through thermal motion

heat - work

change in internal energy =

temperature

the measure of the amount of energy in a substance

inversely

pressure and volume at a constant temperature are ___ related

directly

temperature and volume at a constant pressure are ___ related

quantitation

important to experiments; proved that air is not an element but composed of multiple materials

• Must trap gas to include weight when massing post-reaction

ideal gas law

 a theoretical idea posting that gases take up no space and have no matter

• untrue but can be used as a basis for the behavior of real gases

enthalpy

∆H, measure of how much energy is taken up or released by a chemical reaction when no work is done

second law of thermodynamics

entropy of the universe always increases, so reactions will always proceed in the direction that increases the entropy of the universe

light

Wave argument: 2-slit experiment (interference was present)

Particle argument: light can travel in a vacuum

diffraction

a wave spreads out when it passes through a slit whose size is comparable to its wavelength

2-slit experiment

experiment

helps distinguish between waves and particles because waves will spread out after passing through the slits and particles will align straight with the slits

silk and glass rod

experiment

• Electron transfers change the charge of objects; opposite charges attract each other.

electricity and magnetism

related via: moving magnetic fields make an electric current, and moving electric currents make magnetic fields

electromagnet

electric current is moved repeatedly around a piece of iron which creates a magnetic field and turns the iron into a magnet

dynamo

mechanical forces move magnets in relation to a wire which creates an electric current in the wire

electric field

objects with an electric charge experience a force when they are some distance from other objects with an electric charge

• field strength is directly proportional to the amount of electric charge and inversely proportional to the square of the distance

Maxwell

described constants used to calculate field strength, which it turned out also determined the speed of a wave, which was the speed of light, so he posited that light was a wave of EM field oscillations

EM field oscillations

changing electric and magnetic fields induce each other and propagate through space at the speed of light

visible light

light of wavelengths between long wavelengths (radio, infrared) and short wavelengths (ultraviolet, x-ray, gamma ray)

• EM radiation consists of oscillating electric and magnetic fields; oscillations in one field cause oscillations in the other

• EM interactions are mediated by photons → light is carried by photons

ether

concept developed by Michaelson-Morley; reasoning: waves need to travel through a medium, speed of light must be relative to something

NaCl

experiment: led to the discovery/understanding of the electron; run an electrical current through NaCl → get Na and Cl separately, just by adding/subtracting electrons

cathode ray tube

experiment: led to the discovery/understanding of the electron; shoot electrons through gas from cathode to anode; electric and magnetic fields could change the electrons’ trajectories → electrons have negative charge, we can determine their mass ratios

special relativity

Theory

Addresses that:

• Maxwell: EM waves will always have the same speed of light in a vacuum (constants)

• Galileo: observers moving at different velocities will have different perceptions of the velocities around them

Posits that:

• Light always travels at the same speed in a vacuum

  • Observers will agree on this speed because how they measure time and space is relative to their speed relative to what they’re measuring

• Speed of light is absolute, clocks and measuring sticks are relative

special

included in the name because this theory only works for constant velocities, not accelerations (so we need general relativity)

e = mc_^²

we would observe the ramifications of this equation in any reaction where energy is given off

• If it’s very small-scale, though, you would need very sensitive equipment

force

which requires more __: increasing the speed of an electron from 1% SoL to 10% or 99% SoL to 99.9%?

Increasing the speed of an electron from 99% to 99.9%, because as we approach the speed of light, mass increases exponentially

f = ma

increases in mass are proportional to increases in force required for a set amount of acceleration

charge

determine via: if the particle’s trajectory will bend in an electric field and whether it bends towards the + (if negatively charged) or - (if positively charged)

charge:mass ratio

determine via: let the particle move through electric and magnetic fields that cancel each other’s values (particles will travel in straight lines when velocity = E/B); turn off the magnetic field and let the particle be deflected by the electric field

• the tangent of the angle of deflection will be related to q/m by a coefficient related to the geometry of the apparatus, the voltage of the field, and the velocity you calculated

diffraction

determine via: 2-slit experiment interference pattern

nuclear fission

appears to occur according to strict probabilities; in a set amount of time (e.g. one half-life), a set fraction of the remaining radioactive product will break down (e.g. one half)

alpha

type of emission; essentially fast-moving helium nuclei

beta

type of emission; fast moving electrons or positively-charged, electron-like particles

gamma

type of emission; very high frequency, short wavelength electromagnetic waves

collision

___ of, for example, a fast-moving neutron with a large nucleus, will distort the nucleus enough that the strong interaction will not hold the nucleus together; electromagnetic repulsion can then split the nucleus apart

solar system model

classical model of the atom; tiny, negatively charged electrons orbit a nucleus that contains massive positively charged protons and neutral neutrons; the atom is mostly empty space

• evidence: Rutherford gold foil experiments

• problem: classical physics couldn’t explain why protons would stay in the nucleus

spectra

a gas in the “ground”(unexcited) state will absorb very specific amounts of energy (corresponding to specific wavelengths of light)

• these amounts of energy exactly enable electrons to “jump” from a lower energy level to a particular higher energy level

• the wavelengths absorbed by the atoms give the absorbance spectrum of the atoms and show the differences in energy for different electron “orbitals”

black bodies

objects that can emit and absorb any frequency of EM radiation; emit light of different frequencies in a characteristic pattern depending only on their temperature

ultraviolet catastrophe

classical physics predicted that black bodies should emit ever-increasing amounts of light of higher and higher frequency

• impossible because they would have to emit infinite amounts of energy

• untrue, so there had to be a problem with classical physics

• one of the observations that led to quantum theory.

temperature

highest to lowest in:

white-hot, yellow, red-hot

2-slit

experiment: light behaves as a wave

• if you fire electrons or photons at a piece of material with two slits in it, the electrons or the photons will be detected on the other side as if they were waves: they will exhibit an interference pattern, with alternating dark and light lines instead of having sharp peaks directly in front of each slit

photoelectric effect

experiment: light behaves as particles

• individual photons collide with individual atoms, imparting a set amount of energy (a quantum) to just those atoms they contact

• if the photons have enough energy (depending on their color), electrons are ejected

• electrons behave as particles in cathode rays

Heisenberg uncertainty principle

there are certain pairs of parameters that are related in a very unusual way: the more closely the value of one is constrained, the more the other member of the pair is unconstrained (can take on more values)

• one of these pairs is the amount of energy present in a system and the time for which you are measuring system

• so, systems can deviate greatly from their average energy for very short time

virtual particles

created from the energy of the vacuum and must be “paid back” very quickly

• not detected directly by experiments, but thought to mediate the interactions between particles

• the Heisenberg uncertainty principle relates the energies of the virtual particles to the amount of time they can exist, which determines the range of their effects

n

quantum number; average distance from nucleus when electron is detected

• smaller = closer to nucleus

• 1, 2, 3…

l

quantum number; shape of the volume of space where electrons likely detected

• 0, 1, 2… n-1

m

quantum number; orbital’s orientation in space

• -l to +l

psi

wave function; can be manipulated to tell us everything that can be known about a particle

psi squared

gives the probability of finding an electron in a certain region at a certain time

Schrodinger’s equation

relates psi to the energy of an electron

annihilation

more powerful in top/anti-top than up/anti-up because they have more mass and thus would give off more energy (e=mc^2)

range

short in the strong and weak force, infinite in EM

• Strong: short because mediated by gluons (color charge), which can be easily be absorbed/emit particles, so they can’t last long/travel far despite traveling at the speed of light

• Weak: short because mediated by W and Z bosons, which interact with their own force and are massive, so they can’t travel far fast and are quickly absorbed by or emit other particles

• EM: infinite because mediated by photons, which travel at the speed of light and don’t carry an EM charge

sun

generates positrons and neutrinos by fusion:

• an up quark in one of these protons emits a W+ boson which decays into a positron and a neutrino

• the up quark becomes a down quark as a result (so a proton has become a neutron)

• the neutrino and positron do not experience the strong force, and they escape from the nucleus from which they originated easily

• the neutrinos pour out of the sun in droves

• the positrons find electrons in the sun and annihilate with them, and photons (for the most part) are released that are equivalent to the energy of these two particles

neutron

held together by the strong force that holds the 2 down and 1 up quarks together

decay

enabled by the weak force allowing quarks to switch flavors

• exchange of W particles with other particles interacting with the weak force allows one of the down quarks in the neutron to change to an up quark

pions

comprised of an up and an anti-down or a down and an anti-up of the opposite color (e.g. red and anti-red); exchanged between neutrons and protons, which causes these particles to switch identities within the nucleus of an atom

• this does not change the type of atom because you end up with the same number of each type of nucleon that you started with

• this interaction between nucleons holds them together despite the proton-proton repulsion due to EM

stability

determined by the ratio of protons to neutrons in a nucleus

• at higher molecular weights, you need more neutrons per proton for stability; very high nuclei are intrinsically less stable

  • in part this is because the strong force (which holds nuclei together) is very short-range, while the EM force (which pushes protons apart) is long-range

• so, when nuclei grow bigger, EM becomes more important

grand unified theory/grand unification

electromagnetism and weak interactions have been shown to be different aspects of the same, unified, electroweak force; at high enough temperatures, the effects of these interactions are indistinguishable from each other

• attempt to show that at high enough temperatures, the strong force is also an aspect of this same force

Higgs field

a field whose lowest energy occurs when the field takes on a non-zero value, or in other words, when Higgs particles are present at some level

• standard model predicts that there must be at least one type of Higgs particle, which would be responsible for giving a rest mass to certain particles

• mass of these particles is due to the strength of its interaction with the Higgs particles

gravity

according to the General Theory of Relativity, not a force in the way that EM and the strong and weak interactions are forces, but geometry

• matter and energy move along a curved four-dimensional space-time along their shortest paths

• the curvature of space-time is caused by mass, energy, and pressure, all of which cause space to curve in on itself and contract

• the exception is the when you have a negative pressure, which causes space to expand outward

flat geometry

geometry of the observable universe

• there is a specific critical density of mass-energy in the universe; at precisely this value, geometry is Euclidian

  • parallel lines do not meet, and triangles are 180 degrees

• the universe will continue to increase in volume, but more and more slowly

closed geometry

geometry of the observable universe

• the density is greater than the critical value

• the universe will close in on itself

  • parallel lines move closer together at great distances, and triangles have greater than 180 degrees

• the universe will eventually collapse in a big crunch

open geometry

geometry of the observable universe

• the density is less than the critical density

  • parallel lines grow further apart at great distances, and triangles have less than 180 degrees

• the universe will continue to expand rapidly forever

big bang theory

posits that the universe began very tiny and extremely dense (in terms of energy/matter) andthen exploded outward with enormous force

Hubble

found evidence suggesting the Big Bang theory

• galaxies all around us are red-shifted, indicating that almost everything around us is flying away from us

• more distant objects are flying away faster, which suggests that the universe is expanding

• tracing this idea backward in time suggests that the universe was once much, much smaller

cosmic background radiation

the EM radiation (photons) that we detect uniformly all over space

• the very early universe was very hot and had a high energy density, photons were created and absorbed in high numbers

• for the first three hundred thousand years, the universe was too hot for stable neutral atoms to form, and photons were quickly emitted and absorbed by all the charged particles without being able to escape

• the photons that we actually observe were emitted after the universe became transparent (due to the formation of neutral atoms from a sea of hot charged particles that interacted with photons) about 300,000 yrs after the big bang

  • we detect these as microwaves, which are low in energy, because as the universe expands, the wavelengths of photons stretch with it

hydrogen

main physical origins: energy of Big Bang

helium

main physical origins: first minutes after Big Bang, Hydrogen fusion in hot early universe, cores of main sequence stars

oxygen

main physical origins: red giant cores

uranium

main physical origins: supernovas

inflation

the observable universe appears flat: it seems to possess the amount of energy/matter required for gravity to precisely slow the expansion of space so that the universe will asymptotically approach a final volume

• this is an extremely unlikely result since presumably the universe could contain any amount of matter/energy to start with and since any deviations from this precise value in either direction would be exaggerated over time

• universe appears smooth, which doesn’t make sense because some spaces are so distant that they should never have had time to be in thermal equilibrium with each other if the universe had always been expanding at the current rate

string theory

claims to be a Theory of Everything, adding gravity to forces already unified in the Grand Unified Theory; posits that all particles are actually made of the same, unimaginably tiny (but still finite in length) string that vibrates in different ways to exhibit the characteristics of the different particles

• gravitons described as a necessary consequence of this theory

• because the strings are not infinitesimally small, absurd, infinite solutions to equations are avoided when trying to describe black holes or the early universe

• these infinities are otherwise unavoidable when trying to combine general relativity and quantum mechanics

entropy

∆S, a measure of disorder, the likelihood of an arrangement of molecules, the amount of information needed to exactly specify the state of a system

• higher in large molecules, gases, solutions, metallic bonds

• ___ of products - ___ of reactants

• high eg. oxygen gas

• low eg. oxygen dissolved in water

spontaneity

∆G (Gibbs Free Energy), whether in a certain set of conditions a reaction will go in a certain direction without giving off a net amount of energy

• determines the __ of a reaction

  • Positive: spontaneous, needs to gain more energy

  • Negative: spontaneous, uses energy

• spontaneous reactions increase the entropy of the entire universe

W

the number of different states in which the system can possibly be without changing the energy

le chatelier’s principle

If you “stress” a system at equilibrium, the equilibrium shifts to accommodate the stress.