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ATOMIC AND NUCLEAR PHYSICS

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I love this class so much. It's completely relevant and helpful for my future medical career.

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Leucippus and Democritus

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developed the first concept of the atomic structure of matter -- "all natural bodies consist of infinitely small particles that completely fill the volumes of the bodies/are not further divisible" = ATOMS

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How were the existence of atoms verified?

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By indirect chemistry methods! -- chemists determined the mass ratios of the reactants + reaction products for reactions -- the mass ratios for the same reaction were always the same but different for other reactions

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When was quantitative information about the atom (size/charge distribution) discovered?

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20th century

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When was quantum theory developed?

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1930s

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black body radiation? thermal radiation?

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black body radiation: EM emitted by a black body thermal radiation: CONTINOUS distribution of wavelengths from all portions of the EM spectrum

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Wien's Displacement Law

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-- as temperature increases, wavelength peaks shift to shorter wavelengths basically, -- intensity + amount of radiation emitted increases as temperature increases -- peak wavelength decreases as temperature increases

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Ultraviolet Catastrophe

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in the classical theory of blackbody radiation, the intensity shows to be at infinity with shorter wavelengths; however, experimental results show a giant drop in intensity with shorter wavelengths

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Who developed an equation that "fixed" the ultraviolet catastrophe and and was in agreement with the experimental results of wavelength vs intensity?

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the muthafukin' OG, Planck

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Planks two assumptions regarding blackbody radiation?

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1. blackbody of EM radiation is emitted in SPECIFIC QUANTA (energy is quantized!) En = nfh 2. the oscillators emit or absorb energy when moving between quantum states -- energy carried by the quantum of radiation is... E = hf

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How can quantum energy levels transition?

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One at a time mofo; can't jump from 2-5 .. gotta do 2-3-4-5

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Why is intensity of blackbody radiation low at short wavelengths?

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giant gap in energy levels; low probability of transition

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Why is intensity of blackbody radiation low at long wavelengths?

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small difference between energy levels; many downward movements because of the LOW energy of transitions

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How did the concept of photons come about?

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Einstein rederived Planck's quantum work to create the concept

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Photoelectric effect

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the 2nd unexplainable phenomena - occurs when light incident on certain metallic surfaces causes e- to be emitted from those surfaces

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the emitted e- from the photoelectric effect are PHOTOELECTRONS

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when light is incident on the metal surfaces, a current is detected from the "emitted plate" to the "collector" in the dark, there is no current

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How are voltage values related to the current?

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- at large voltage values, current reaches a maximum - maximum current increases as intensity of light increases - when voltage is less the the stopping potential (delta Vs), current = 0

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Stopping potential

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depends on kinetic E defined as: potential E necessary to stop any e- from reaching the "collector"

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What do we know about the dependence of photoelectron kinetic E on light intensity?

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it is NOT dependent on light intensity it IS dependent on stopping potential, frequency and work function

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What do we know about the dependence of ejection of e- on light frequency?

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it is dependent on a certain cutoff frequency -- no e- are ejected below this frequency regardless of intensity

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What do we know about the dependence of photoelectron kinetic E on light frequency?

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max kinetic energy of the photoelectrons increases with increasing light frequency

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Einstein extended Planck's concept of quantization to EM waves. What did he conclude?

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All EM radiation can be considered a stream of quanta = PHOTONS

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Work function

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minimum E with which an e- is bound in the metal - metals have higher work function (PHI) then nonmetals Kmax = hf - PHI (work function) - photon must have more energy than work function in order to eject an e-

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How is cutoff frequency and cutoff wavelength related?

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at wavelengths greater than the cutoff wavelength, there is no emission of photoelectrons cutoff wavelength = hc/ PHI *** application: burglar alarm systems

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Why was classical wave theory shit?

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it failed to explain the SCATTERING of x-rays from e-

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let's talk a bit about the Compton Effect

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according to classical predictions, EM waves incident on an e- should cause it to accelerate in an oscillating motion (many FREQUENCIES) ... well that's WRONG what actually happens: only one frequency is observed meaning that the e- moves in a straight line (particle like!) hence, the scattering of these e- (scattered radiation form he photon-electron collision) : COMPTON EFFECT

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Compton shift equation

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-- at different angles, scattered x-rays peak at different points (shifts) -- caused by SCATTERING OF E- !!! wavelength (final) - wavelength (initial) =[h/Me * c](1-cos(theta)) Me = mass of electron

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So, is light a wave or a particle?

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bahahahaha, it's both! the photon and wave models complement each other <3

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the quantum particle:

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-- new model that is the result of the recognition of the dual nature of both light and material particles -- entities have both particle and wave characteristics

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Ideal wave

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single frequency and is infinitely long (UNLOCALIZED in space)

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Ideal particle

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has zero size (is LOCALIZED in space)

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What's the deal with particles as wave packets?

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concept: multiple waves can be superimposed so that at x=0 there is constructive interference - at any other point, interference is destructive -- small region of constructive interference constitutes a WAVE PACKET --> identified as a PARTICLE

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Double-slit experiment

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showed that light acts as a particle and a wave 1. e- are detected as particles at a localized spot at some instant of time 2. probability of arrival at that spot is determined by finding the intensity of 2 interfering waves

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Uncertainty principle

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impossible to make simultaneous measurements of a particle's position and momentum with infinite accurary

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Emission Spectroscopy

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"all objects emit thermal radiation characterized by a continuous distribution of wavelengths" basically, when an electron on an atom gives off energy by going down an energy level, it will emit a certain color each atom has a unique emission spectrum and this technique can be used to identify elements in unknown compounds

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Absorption Spectroscopy

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when an electron absorbs energy by going up an energy level, it will absorb the light/colors that it emits when going down an energy level

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"shorter wavelengths are higher E (purple)"

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"longer wavelengths are lower E (red)"

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Thompson's model of the atom

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"plum pudding model" - e- embedded in a positive volume - *** discovered the e-

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Rutherford's model of the atom

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"thin foil experiment" - proved there was a positive nucleus - thought that e- spin in circles with centripetal acceleration until they disappear into the nucleus

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Bohr's model of the atom

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- applied Planck's ideas of quantized energy levels to Rutherford's orbiting e-

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Bohr's postulates

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1. e- orbit around nucleus like planets in a solar system 2. only certain e- orbitals are stable (e- no not continuously emit energy/do not spiral into the nucleus) 3. radiation is emitted when e- moves to a lower E state and vice versa for absorbed radiation 4. size of allowed e- orbit depends on angular momentum -- radii of allowed orbits have discrete values (QUANTIZED)

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What is the lowest energy level of an atom?

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ground state; n=1 ; Bohr's radius *** ** as n increases, energy increases and becomes less negative **

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Uppermost atomic energy level?

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n = infinity; E = 0 ** beyond this point, e- gets ionized meaning that it "jumps" off the atom

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Atomic number?

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Z; # of protons in a nucleus

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What were some difficulties with the Bohr model?

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- it cannot account for the spectra of more complex atoms - scattering experiments showed that the e- in an atom does not move in flat circles; they move in spheres (3D)

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What are the 4 quantum numbers/states?

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(n) principle quantum number (l) orbital quantum number (n-1) (ml) magnetic quantum number (2l+1) (ms) spin quantum number (+.5 or -.5)

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What are shells and subshells?

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- states having same n form SHELLS - states having same n and l form SUBSHELLS

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Zeeman effect

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spectral lines splitting up under an external magnetic field (n --> ml numbers)

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Wave function

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probability of finding an e- as a function of distance from the nucleus

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Electron clouds

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area around nucleus of an atom where e- are most likely to be found (darkest around the nucleus -- means more e- are probably going to be found there)

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Pauli Exclusion Principle

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- no two e- can ever in the same quantum state; no 2 e- in the same atom can have the same set of quantum numbers - only 2 e- can be present in any orbital (one with spin up and spin down)

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Hund's Rule

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- max number of e- are unpaired when placing them

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What are x-rays?

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they are the result of the slowing down of high energy e- as they strike the metal target

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Stimulated Absorption

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- when a photon has energy equal to the difference in energy levels, it cab be absorbed by the atom - absorption of photon causes some of the atoms to be raised to exited states

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Spontaneous Emission

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excited atom falls to ground state (lower E level)

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Stimulated Emission

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when excited state is a metastable state (aka, lifetime is much longer than the typical 10e^-8 s) *incident photon causes e- to go to ground state whiteout being absorbed

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L.A.S.E.R.

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"light amplification by stimulated emission of radiation"

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What is a nucleus composed of?

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protons and neutrons

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A = Z + N is what?

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A = mass number Z = number of protons N = number of neutrons

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Mass number DOES NOT equal atomic number

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ya dig?

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Isotope

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"elements that have same Z but different N and A values" - different number of neutrons

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Size of the nucleus...

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Was discovered by Rutherford; he used the isolated energy system to find "d" d = distance of closest approach (two positive charges coming together) radius of nucleus = 10e^-14 m

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Fermi

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(fm); about 10e^-15 m

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Average radius of nucleus equation

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r = aA^1/3 a = constant; 1.25e^-15 A = mass number

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Why don't the large repulsive electrostatic forces between proteins cause the nucleus to fly apart?

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because of nuclear force -- attractive force between all nuclear particles

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When are light nuclei most stable? Heavy nuclei?

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for light nuclei, when N=Z for heavy nuclei, when N>Z N = neutron number Z = atomic umber *** as the number of protons increases, the coloumb repulsive force increases so more neutrons are needed to keep the nucleus stable

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Binding Energy

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difference of total energy of the bound system (the full nucleus) and the combined E of the separated nucleons (it is less) -- amount of E you need to add to break up the nucleus EQUATION: Eb = [ZM(H) + Nmn - M (azX)] x 931.49 MeV/u M(H) = mass of neutral H atom M (azX) = mass of an atom of its isotope mn = mass of neutron

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Why is E released when a heavy nucleus splits of FISSIONS?

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... because nucleons in product nucleus are more tightly bound then in original nucleus

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Nuclear models

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1. liquid drop model 2. shell model

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Shell Model

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"proton E level are further apart than those for neutrons due to the superposition of the Coulomb force and the nuclear force for the protons" -- nuclei with even number of protons and neutrons are most stable -- nuclei tend to have more neutrons than protons (proton energy levels are higher so adding more neutrons than protons is more energetically favorable"

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Radioactivity

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"spontaneous emission of radiation" --> result of the decay/disintegration of unstable nuclei

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Three types of decay

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1. alpha (neutron rich) - can be stopped by a thick piece of paper 2. beta (proton rich) - can pass through a foil of lead or a plate of aluminum 3. gamma (very proton rich) - high E photons, can pass through a thick wall of concrete

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Alpha Decay

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" nucleus loses 2 protons and 2 neutrons" - daughter nucleus has two less neutrons and protons - alpha particle is Helium! (has 2 protons and 2 neutrons)

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Alpha decay is SPONTANEOUS DECAY what does this mean?

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= the nucleus of one element changes with then nucleus of another *** total number of protons and neutrons is unchanged in this fission

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Disintegration Energy (the Q value)

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Q = (Mx - My - Malpha) c^2 Mx = mass of original nucleus My = mass of daughter nucleus Malpha = mass of alpha particle c= speed of light

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Radioactive series

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often, daughter nucleus is unstable and decays as well --> and so on, so forth *** stops when it reaches a stable isotope

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Application of alpha decay -- SMOKE DETECTOR

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-- components: ionization chamber, sensitive current detector, alarm 1. a weak radioactive source ionizes the air in the chamber of the detector, creating charged particles 2. voltage is painted between the plates inside the chamber 3. if smoke drifts into the chamber, the ions become attached to the smoke particles 4. this causes a decrease int eh detector current, setting off the alarm

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Beta Decay

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"daughter nucleus has the same number of nucleons (atomic mass) as the parent, but the atomic number is changed by 1" basically, beta decay occur when, in a nucleus with too many protons or neutrons, one of the protons or neutrons is transmitted into the other ** will sooner or later produce gamma rays **

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Beta Minus Decay

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neutron decays into a proton, an e- and an antineutrino (add to Z)

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Beta Plus Decay

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proton decays into neutron, a positron (e+) and a neutrino (subtract from Z)

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4 fundamental forces

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gravitational, electromagnetic, strong force, weak force

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Gamma Decay

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"occurs when an excited nucleus emits a high E photon" -- only thing that changes is nucleus' E state, goes to a lower one -- usually alpha or beta decay precedes gamma emission because they result in an excited state

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3 natural occurring radioactive elements?

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uranium, actinium, thorium

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The Decay Constant

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lambda (decay constant) = 0.693/T1/2 T1/2 = time at half life

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The Decay Rate

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R = R naught * e^lambda t R naught = decay rate at t=0 lambda = decay constant

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Half Life Equation

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N = N naught * (1/2)^n N = undecayed radioactive nuclei remaning n = number of half lives

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