Cathode Ray Experiments
cathode ray - free electrons emitted by a negative electrode
these rays could be deflected by a magnetic field
J.J. Thomson (1897)
proved more clearly that cathode rays carry negative charge
hypothesis on why rays couldn’t be deflected with an electric field —> cathode rays ionized some of the air molecules remaining in the vacuum chamber and these ions shielded the cathode rays from the electric field
by trying to get an extremely low pressure in the tube, he demonstrated that cathode rays respond to electric fields as negatively charged particles would —> discovered the electron
Charge-to-mass Ratio of the Electron
Thomson did not have a method for measuring mass or charge of an electron
he found a way to determine ratio of charge to mass for electron using both an electric and magnetic field
Fe = qE and Fm = qvB
Fnet = Fe + Fm
Fnet = 0
Fe = Fm
Eq = qvB
E = Bv
v = E/B —> speed for a particle
Thomson used mutually perpendicular electric and magnetic fields to determine speed of cathode rays and measured deflection when one of the fields was switched on
deflections depended on the magnitude of the field, the length of the path in the field, the speed, charge and mass of cathode ray particles
used his measurements to calculate a ratio of 2 unknowns, q and m
concluded that all cathode rays consisted of identical particles with exactly the same negative charge
experiments showed that q/m ≈ 1011 C/kg
Thomson reasoned that electrons are much smaller than atoms and put forward a theory that atoms were divisible and that the tiny particles in cathode rays were “the substance from which all chemical elements are built up”
Determining Charge-to-mass Ratios
when a charge particle moves perpendicular to a magnetic field, the magnetic force is perpendicular to the particle’s velocity so particle’s direction changes but its speed is consistent
a charge particle moving perpendicular to a uniform magnetic field follows a circular path, with magnetic force acting as the centripetal force
Fnet = Fm
Fc = Fm
(1/r)mv2 = qvB
q/m = v/Br
Thomson’s Raisin-bun Model
most atoms are electrically neutral
if electrons are constituents of atoms, atoms must also contain some form of positive charge
since no positively charged particles had been discovered Thomson suggested that atoms might consist of electrons embedded in a blob of massless positive charge
Millikan’s Oil Drop Experiment
used an atomizer to spray tiny drops of oil into the top of a closed vessel containing two parallel metal plates
friction during the spraying process gave some of the oil drops a small electric charge, Millikan also used x-rays to charge oil drops
was able to calculate mass, connected high voltage battery to the plates and observed motion of oil drops in a uniform electric field
by analyzing motion and allowing for air resistance, he calculated force acting on each drop and then determined charge on the drop
found that charged oil drops have a charge by gaining or losing an electron, therefore the charge is 1.60 × 10-19 C/e-
showed that a charge is not a continuous quantity, it exists only in discrete amounts
with Thomson’s ratio and his value of charge, it was possible to find the final mass
Rutherford’s Scattering Experiment
Ernest Rutherford (1871-1937) was fascinated by radioactivity
by 1909 he had shown that some radioactive elements emit positively charged helium ions or alpha particles
he observed that a beam of these particles spread out somewhat when passing through a thin sheet of mica
had two assistants, Hans Geiger and Ernest Marsden measure proportion of alpha particles scattered at different angles from various materials
shot alpha particles at gold foil and measured scattering angles
most of the alpha particles travelled through the foil with a deflection of a degree or less
the number of alpha particles deflected dropped off drastically as the scattering angle increased
a few alpha particles were scattered at angles greater than 140° and once in a while an alpha particle would almost bounce straight back
concluded that the positive charge in a gold atom must be concentrated in an incredibly tiny volume
Rutherford showed that the positive charge and most of the mass of an atom are contained in a radius of less than 10-14 m
discovered nucleus and disproved raisin bun model
Planetary Model/Nuclear/Rutherford Model
electrons orbit the nucleus like planets orbiting the sun
electrostatic attraction between positive nucleus and negative electrons provides the centripetal force that keep the electrons in their orbits
Bohr Model of the Atom
in 1912, Niels Bohr (1885-1962)
Bohr and Rutherford recognized a critical flaw in planetary model
experiments had shown that accelerating charges emit EMR (James Maxwell Clerk)
electrons are constantly accelerating so they should emit EMR
these waves would take from the orbiting electrons and the electrons would spiral into the nucleus in microseconds
Bohr, through Planck’s concept of quantized energy may provide a different solution
this led to the basis of spectroscopy - study of light emitted and absorbed by different materials
Spectroscopy
in 1814, Josef von Fraunhofer notices a number of gaps or dark lines
by 1859, Gustav Kirchhoff had established that gases of elements or compounds under low pressure each have a unique spectrum
Kirchhoff’s laws for spectra explain how temperature and pressure affect the light produced or absorbed by the material:
a hot, dense material emits a continuous spectrum, without any dark or bright lines
a hot gas at low pressure has an emission line spectrum with bright lines at distinct characteristic wavelengths
a gas at low pressure absorbs light at the same wavelengths as the light it emits when heated, shining light through the gas produces an absorption line spectrum with dark lines that match the bright lines in the emission spectrum for the gass
Emission line spectrum - a pattern of bright lines produced by a hot gas at low pressure
Absorption line spectrum - a pattern of dark lines produced when light passes through a gas at low pressure
Spectrometer - a device for measuring the wavelengths of light in a spectrum
Bohr Model of the Atom (1913)
electrons can orbit nucleus only at specific distances, these distances are particular multiples of the radius of the smallest permitted orbit, therefore the orbits in an atom are quantized
this model only works for hydrogen
kinetic energy and potential energy of an electron in orbit depends on an electron’s distance from the nucleus, therefore the energy of an electron is also quantized, each orbit corresponds to a particular energy level for an electron
an electron can move from one energy level to another by emitting or absorbing energy equal to difference between energy levels, an electron that stays in particular orbit does not radiate energy, since size and shape of orbit remain constant along with energy of the electron, the orbits are often called stationary states
Energy level - a discrete and quantized amount of energy
Stationary state - a stable state with a fixed energy level
Principal quantum number - the quantum number that determines the size and energy of an orbit
Energy Level Transition and Line Spectra
Bohr model explains why absorption and emission line spectra occur
to jump to a higher energy level, an electron must gain energy, it can gain this energy by absorbing a photon
for energy to be conserved, the photon’s energy must match the change in energy between levels, therefore the atom can only absorb frequencies that correspond to the difference of energy of the atom’s energy levels
absorption of light at these specific frequencies causes the discrete dark lines in absorption spectra
atoms can also only emit photons corresponding to change in energy between levels
when an electron in an atom absorbs a photon, the final energy level of the atom’s electron is higher than initial energy level
using law of conservation of energy: Ephoton= Efinal- Einitial
Failings of Bohr Model
does not really explain why energy is quantized, nor why orbiting electrons don’t radiate electromagnetic energy
it is not accurate for atom that have two or more electrons
it does not explain why a magnetic field splits the main spectral lines into multiple closely spaced lines, discovered by Pieter Zeeman in 1896 - Zeeman effect
Wave Nature of Electrons
in 1924, Louis de Broglie developed theory that particles have wave properties
diffraction experiments confirmed that electrons behave like waves that have wavelengths, as predicted by de Broglie
the principles of interference and standing waves apply for electrons orbiting a nucleus
Quantum Indeterminacy
the quantum model does not have electrons orbiting at precisely defined distances from the nucleus
electrons behave as waves, which do not have a precise location
the orbitals in quantum model show the likelihood of an electron being at a given point, they are not paths that the electrons follow
the idea that electrons within an atom behave as waves rather than as orbiting particles explains why these electrons do not radiate electromagnetic energy continuously
The Nucleus
scattering experiments directed by Rutherford showed that more than 99.9% of the mass of an atom is concentrated in a nucleus that is typically only a few femto meters (10-15m) in diameter
in 1918, Rutherford concluded that hydrogen nucleus was a fundamental particle that is a constituent of all nuclei - protons
in 1920, Rutherford suggested that nuclei might also contain neutrons
in 1932, James Chadwick was able to isolate neutrons and determined that the mass of a neutron is about 0.1% greater than mass of a proton
Isotopes - atoms that have the same number of photons but different numbers of neutrons
Atomic mass unit is exactly 1/12 of mass of carbon-12 atom (1.66 × 10-27 kg)
Strong Nuclear Force
the force that binds together the protons and neutrons in a nucleus
very short range
more powerful than electrostatic force within a nucleus
has negligible effect on particles more than a few femtometers apart
acts on nucleons, does not affect electrons
Binding Energy and Mass Defect
removing a nucleon from a stable nucleus requires energy due to work being done to overcome strong nuclear force
binding energy (Eb) - the net energy required to liberate all of the protons and neutrons in a nucleus
Eb is the difference between the total energy of the separate nucleons and the energy of the nucleus with nucleons bound together
Eb = Enucleons - Enucleus
E = mc2
nuclear reactions can involve conversions between mass and energy - law of conservation of energy still applies if conversions are taken into account
mass defect - the difference between the sum of the masses of the separate nucleons and the mass of the nucleus
Δm = mnucleons - mnucleus
Radioactive Decay
Antoine Henri Becquerel (1852-1908) discovered radioactive decay in 1896 while conducting experiments with uranium
found that uranium emitted radiation and that a magnetic field would deflect some of this radiation
Marie and Pierre Curie began extensive research on radiation and discovered new radioactive elements
she found that intensity of radiation from uranium compounds was not affected by the other elements in the compound or by processes such as being heated, powdered or dissolved, intensity depended on the quantity of uranium
Rutherford and other identified 3 forms of nuclear radiation:
alpha (∝) - the emission of a helium nucleus
beta (β) - the emission of a high-energy electron
gamma (γ) - the emission of a high-energy photon
three types of radiation result from different processes within nuclei
alpha particles typically do not penetrate much more that metal foil or a sheet of paper
beta particles can pass through up to 3mm or aluminum
gamma rays can penetrate several centimeters of lead
Conservation Laws and Radioactive Decay
conservation of charge - net electrical charge cannot change in a decay process, any charge in the electrical charge of the nucleus must be exactly offset by an opposite charge elsewhere in the system
conservation of atomic mass number - the total of the atomic mass numbers for the final products must be equal to the atomic mass number of the original nucleus, total number of nucleons remains constant
Alpha Decay
1908, Rutherford showed that alpha particles are helium nuclei spontaneously emitted by unstable large nuclei
electromagnetic force in nuclei is repelling the outer protons and is almost as great as great as the strong nuclear force
a cluster of 2 protons and 2 neutrons forms a highly stable helium nucleus, these unstable large nuclei decay by emitting alpha particles rather than separate protons and neutrons
parent element (X) - the original element in decay process
daughter element (Y) - the element produced by a decay process
Beta Decay
nucleus decays by emitting an electron
beta-negative decay - nuclear decay involving emission of an electron
a neutron in the nucleus transforms into a proton, electron and antineutrino
atomic number of the nucleus increases by 1, but atomic mass number doesn’t change
charge is conserved because the charge on the new proton balances the charge on the electron emitted from the nucleus (the beta particle)
measurements found that most electrons emitted during beta decay had somewhat less kinetic energy than expected, and few had almost no kinetic energy
in 1930, Wolfgang Pauli suggested that the missing energy was carried away by a tiny, neutral particle - neutrino
neutrino - and extremely small neutral, subatomic particle
in beta-negative decay an antineutrino is released, in beta-positive decay a neutrino is released
neutrino and antineutrino are identical in all aspects except for their opposite spins
the transformation of a neutron into a proton involves the weak nuclear force
weak nuclear force - fundamental force that acts on electrons and neutrinos
beta decay involves antimatter
antimatter - form of matter that has a key property, such as charge, opposite to that of ordinary matter
beta-positive decay - nuclear decay involving emission of a positron
a proton transforms into a neutron and the parent nucleus emits a positron and a neutrino
Gamma Decay
emission of a high-energy photon by a nucleus
in excited states, nucleons are farther apart, therefore their binding energy is less than when in the ground state and total energy of nucleus is greater
when making a transition to a lower-energy state a nucleus emits a gamma-ray photon
gamma decay does not change the atomic number or atomic mass number
often alpha or beta decay leaves the daughter nucleus in a highly excited state
the excited nucleus then makes a transition to its ground state and emits a gamma ray
the energy of a gamma ray depends on the energy levels and the degree or excitation of the particular nucleons
gamma rays can have energies ranging from thousands to millions of electron volts
Stability of Isotopes
as atomic number increases, the isotopes require an increasing ratio of neutrons to protons in order to be stable
there are no completely stable isotopes with more than 83 protons
stable isotopes have greater binding energies than unstable isotopes
radioactive decay transmutes unstable nuclei into nuclei with higher binding energies
transmute - change into a different element
Radioactive decay series - process of successive decays that continue until it creates a stable nucleus
Radiation Types and their Effects
Half-life (T1/2)
time required for one-half of the radioactive nuclei in a sample to decay
N = N0(1/2)t/t(1/2)
Fission
when a nucleus with an atomic mass number greater than 120 splits into smaller nuclei, they have a greater binding energy per nucleon
gives off energy equal to the the difference between the binding energy of the original nucleus and total binding energy of the products
Fusion
when 2 low-mass nuclei combine to form a single nucleus with atomic mass number less than 60
nucleosynthesis - formation of elements by the fusion of lighter elements
resulting in a more tightly bound nucleus
fusion reaction gives off energy equal to the difference between the total binding energy of the original nuclei and the binding energy of the product
Change in energy for both fission and fusion reactions can be calculated with: ΔE = Ef - Ei
Nuclear Fission
often results from a free neutron colliding with a large nucleus
nucleus absorbs the neutron forming a highly unstable isotope that breaks up almost instantly
Cloud Chambers
device that uses trails of droplets of condensed vapor to show the paths of charged particles
contains dust-free air supersaturated with vapor from a liquid such as water or ethanol
vapor amount depends on temperature and pressure
liquid and vapor in cloud chamber are not in equilibrium and a tiny disturbance can trigger condensation of vapor into droplets or liquid
a charged particle speeding through the supersaturated air will ionize some molecules along its path
ions trigger condensation, forming a miniature cloud along trajectory of the speeding particle
Charles Thomson Rees Wilson made first observations of particle tracks in cloud chamber in 1910
Bubble Chamber
uses trail of bubbles in a superheated liquid to show the paths of charged particles
developed in 1952 by Donald Gleser
contains a liquified gas, like hydrogen, helium, propane or xenon
lowering pressure in the chamber lowers boiling point of liquid
when pressure is reduced so that the boiling point is just below the actual temperature of the liquid, ions formed by a charged particle sipping through liquid will cause it to boil
the particle will form a trail of tiny bubbles in its path
reverse process of cloud chambers, particles tracks formed by liquid turning to vapor vs. vapor turning into liquid
Neutral particles will not create tracks in a cloud or bubble chamber
Fundamental particle - a particle that cannot be divided into smaller particles, an elementary particle
Antimatter
in 1932, Carl Anderson provided the first evidence that antimatter really does exist
he photographed a cloud chamber track of a positron
quantum theory predicts that each kind of ordinary particle has a corresponding antiparticle
a collision between a particle and its antiparticle can annihilate both particles and create a pair of high-energy gamma-ray photons travelling in opposite directions
e+ + e- —> 2γ
Annihilate - convert entirely into energy
Quantum Field Theory
a field theory developed using both quantum mechanics and relativity theory
mediating particles are the mechanics by which the fundamental forces act over the distance between particles
particles that mediate a force exist for such a brief time that they cannot be observed
mediating particle - a virtual particle that carries one of the fundamental forces
virtual particle - a particle that exists for such a short time that it is not detectable, for these particles, energy, momentum and mass are not related as they are for real particles
concept of mediating particles was first applied to electromagnetic force in quantum electrodynamics theory
quantum electrodynamics - quantum field theory dealing with the interactions of electromagnetic fields, charged particles and photons
theory states that virtual photons exchanged between particles are the carriers of the attractive or repulsive force between the particles
Mediating Particles
by 1970, research led physicists to suggest that strong nuclear force is mediated by zero-mass particles called gluons
gluon - mediating particles for the strong nuclear force, there is indirect evidence for their existence
weak nuclear force is mediated by 3 particles: W+, W-, Z0, detected in 1983
graviton - the hypothetical mediating particle for the gravitational force
Primary cosmic rays - high-energy particles that flow from space into Earth’s atmosphere
Secondary cosmic rays - the shower of particles created by collisions between primary cosmic rays and atoms in the atmosphere
Muon - an unstable subatomic particle having many of the properties of an electron but a mass 207x greater
Pion - an unstable subatomic particle with a mass roughly 270x greater than that of an electron, much less stable than muons and have some properties unlike those of electrons, protons and neutrons
2 separate families of particles:
Leptons - subatomic particle that does not interact via the strong nuclear force, much smaller diameter than hadrons
Hadrons - subatomic particle that does interact via the strong nuclear force, 2 subgroups of hadrons:
Mesons - a hadron with an integer spin
Baryons - a hadron with a half-integer spin
Spin - a key quantum property resembling rotational angular momentum, can either be an integer or half-integer multiple of Planck’s constant divided by 2π, can affect the interactions and energy levels of particles
Fermions - particle with half-integer spin
Boson - particle with integer spin
Leptons and baryons are fermions
Mesons and mediating particles are bosons
The Quark Model
in 1963, Murray Gell-Mann and George Zweig proposed that all hadrons are composed of simpler particles - quarks
quarks - any of the group of fundamental particles in hadrons
they showed that all the hadrons known could be made from just three smaller particles and their antiparticles (up quark, down quark, strange quark)
this theory required that quarks have fractional charges that are either -1/3 or +2/3
quark model accurately predicted key aspects of electron-positron interactions
pattern of scattered electrons in an experiment in 1967, suggested that the mass and charge of a photon are concentrated in three centers within the proton
in quark model, protons and neutrons contain only up and down quarks
strange quark accounts for the properties of strange particles —> hadrons that decay via the weak nuclear force even though they originate from and decay into particles that can interact via the strong nuclear force
1974 charm quark, 1977 bottom quark, 1995 top quark
individual quarks probably cannot be observed
the energy required to separate quarks is large enough to create new quarks or antiquarks that bind to the quark being separated before it can be observed on its own
Composition of Protons and Neutrons
protons and neutrons contain only first-generation quarks
protons consist of a down quark and two up quarks
neutrons consist of two down quarks and one up quark
Composition of Other Hadrons
all of the hadrons discovered in the 20th century can be accounted for with a combination of either two or three quarks
all the mesons consist of a quark and an antiquark
all the baryons consist of three quarks
all the antibaryons consist of three quarks
experiments in 2003 produced strong evidence that the theta particle consists of 5 quarks
Beta Decay Using Quarks and Leptons
physicists think that the down quark emits a virtual W- particle (a mediator for the weak force) that then decays into an electrons and antineutrino
similarly in beta-positive decay, an up quark of a proton turns into a down quark
The Standard Model
the current theory describing the nature of matter and the fundamental forces
all matter is composed of 12 fundamental particles, the 6 leptons and 6 quarks and their antiparticles
the electromagnetic force and the weak nuclear force are all both aspects of a single fundamental force - theory of electro weak force, it predicted existence and masses W+, W-, Z0 particles
the electromagnetic and nuclear forces are mediated by virtual particles; the photon, gluon, W+, W-, and Z0 particles
all quarks have quantum property termed color, which determines how the strong nuclear force acts between quarks
the quantum field theory describing the strong nuclear force in this way is called quantum chromodynamics
quantum chromodynamics - quantum field theory that describes the strong nuclear force in terms of quantum color
