the nucleus of the atom · 2009. 1. 9. · the nucleus of the atom in 1919, rutherford starts to...
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The nucleus of the atom In 1919, Rutherford starts to
collect the first data indicatingthat there is another structurewithin the nucleus- the proton.
Two years later, JamesChadwick and E.S. Bielerconclude that some strongforce holds the nucleustogether.◆ Why? If protons in nucleus
(and not electrons) thenwhat keeps the repulsiveforce from driving thenucleus apart?
◆ Nucleus confined to a verysmall volume (<10-14 m indiameter), 0.01% ofdiameter of atom
▲ density is 1017 kg/m3
So here we are in 1930 There were three fundamental
particles- electron, proton, andphoton.
There were three fundamentalforces- gravity,electromagnetic, and thestrong nuclear force.
Gravity we know is muchweaker than the other forces◆ strong force is about 100X
stronger than EM force▲ naturally occuring
elements only have up to100 protons
▲ strong force betweenprotons saturates but EMrepulsive force doesn’t
▲ for more than 100protons repulsive forcewins
There were still some“details” to work out butmany felt like Max Born,who said, "Physics as weknow it will be over in sixmonths."
◆ Who is Max Bornsgranddaughter ?
Olivia Newton-John◆ as far as I know, John
Travolta is not relatedto any famousphysicist
The nucleus
The nucleus hadceased to befundamental. It wascomposed ofpositively chargedprotons and neutrallycharged neutrons(not actuallydiscovered until 1931by Chadwick).
Characterizing atoms
Nuclei of atoms consistof protons and neutrons
Surrounding the nucleusare the electrons
Characterize nuclei byfollowing characteristics◆ Atomic number Z: # of
protons in nucleus (alsoequal to # electrons fornormal atom)
◆ Neutron number N: # ofneutrons in nucleus
◆ Mass number A: # ofnucleons (protons +neutrons) in nucleus
AZX : X is symbol for
element, A is atomicmass and Z is atomicnumber
Isotopes of an elementhave the same atomicnumber but differentatomic weight◆ same number of protons
and electrons▲ same chemical properties
◆ different number ofneutrons
▲ different nuclearproperties
Masses
note the factor of 2000difference
unified mass unit: 12C has a mass of 12 amu1 u = 1.660559 X 10-27 kg
ER = mc2
Radius of nucleus
Rutherford found anexpression for how closean alpha particle cancome to a nucleus
For a head-on collisionall of kinetic energy ischanged to potentialenergy◆ 1 2 (2e)(Ze)
2 mv = k d◆ d is the distance of closest
approach
Solve for d 4kZe2
d = mv2
…or a distance of about 3.2 X10-14 m for alpha particles ona gold nucleus
From these results, Rutherfordconcluded that the positivecharge in a nucleus isconcentrated in a spherewhose radius is no greaterthan ~10-14 m or about 10fermis (1 fermi = 1 X 10-15 m)
Nuclear radii go as:◆ r=roA1/3
◆ A is the # of nucleons andro=1.2X10-15 m
◆ all nuclei have roughly thesame density
Stable nuclei The nucleus can exist only
because the strong nuclearforce between nucleons in anucleus is stronger than theelectrostatic repulsive forcebetween the protons
Light elements have roughlythe same number of protonsand neutrons
Heavier elements have moreneutrons than protons(neutrons contribute to thestrong binding force inside thenucleus but not to therepulsive EM force)
Isotopes within the shadedregion are stable
Unstable nuclei The heavier elements in the
universe were all made insupernova explosions
Unstable isotopes areproduced (too many neutrons)which then decay to the stableisotopes
One of areas of concentrationof NSCL (and of RIA)
Binding Energy
The total mass of anucleus is less than thesum of the masses of theprotons and neutronsthat comprise it
This difference is calledthe binding energy of thenucleus and can bethought of as the energythat must be added to anucleus to break it apart
iron has the highest binding energy
Radioactivity In 1896, Henri Becquerel, while
investigating fluoresence inuranium salts, accidentallydiscovered radioactivity
Work by Curies and othersshowed that radioactivity was theresult of the decay ordisintegration of unstable nuclei
Up til that point, atoms werebelieved to be indestructible andforever
Cleared up a major question as towhy the interior of the Earth wasstill molten
Shared the 1903 Nobel prize withthe Curies
Work by Curies and othersshowed that radioactivity was theresult of the decay ordisintegration of unstable nuclei
Radiation
Alpha particles arehelium nuclei (2 p, 2n):
Beta particles arespeedy electrons:
Gamma radiation is astream of photons:
these are supposed tobe x’s
Half-life If a radioactive sample
contains N radioactive nucleiat some instant, the number ofnuclei that decay in a time Δtis proportional to N◆ ΔN/Δt α N◆ ΔN = -λNΔt◆ where λ is a decay
constant R = |ΔN/Δt| = λN
◆ rate of which atoms decay N=Noe-λt
T1/2 (half-life) is time it takesfor half of sample to decay
Decay constants vary greatlyfor different radioactivedecays and thus so do half-lives
Alpha decay
A A-4 4ZX Z-2
Y + 2He
X is called the parent nucleusand Y the daughter nucleus
Example is Radium, decayinginto Radon and an alphaparticle
In order for alpha emission tooccur, mass of the parentmust be greater thancombined mass of daughterand alpha particle◆ excess mass converted into
kinetic energy, most of whichis carried by the alpha particle
Beta decay
When a radioactivenucleus undergoes betadecay, the daughternucleus has the samenumber of nucleons asthe parent nucleus buthe atomic number ischanged by 1◆ A A - ZX Z-1
X + e
A neutron turns into aproton emitting anelectron◆
10n 11p + e-
One problem: expect the electronto carry away almost all of the kinetic energy but it doesn’t
It has a range of energies.
Problemo, big problemo Is Momentum Conserved? How can we account for the
discrepancies? Wolfgang Pauli suggested a
bizarre idea, another particle, onenot yet seen, was carrying themissing energy and could beused to solve the momentumissue.
For Conservation of Charge, thenew particle would have to beneutral.
According to other experiments,the particle would have to beincredibly light, perhaps even bemassless!
A joke name but it stuck
Due to thosecharacteristics, theItalian physicistEnrico Fermisuggested calling it
Neutrino
Italian for “littleneutral one.”
-zero electric charge-very small mass (if any)-a spin of 1/2-very weak interaction with matter,making it difficult to detect
New interaction force
Since the beta decayhappened to freeneutrons outside thenucleus, the StrongNuclear Force could notbe responsible.
Thus physicists were ledto consider anotherfundamental force- theWeak Nuclear Force.
At this point, there were◆ Five Fundamental
Particles: electron, proton,neutron, electron, photon,and neutrino.
◆ and Four FundamentalForces (or Interactions):Gravity, Electromagnetic,Strong Nuclear Force, andWeak Nuclear Force.
The Weak Force isweaker thanElectromagnetic orStrong, but is strongerthan Gravity.
Mass of neutrinos Not until 1956 was there
convincing experimental evidencethat neutrinos really existed. Anexperiment at a nuclear reactorconducted by Fred Reines wasable to measure interactionsresulting from neutrinos. Whywas this so difficult? Because theneutrinos only interacted via theweak force. The incredibly vastmajority of them passed throughthe detector without leaving anytrace.
Currently there’s an experiment inJapan called Kamland which isdesigned to detect neutrinos fromJapan’s working nuclear powerplants
Solar neutrinos The nuclear reactions in the Sun
produce neutrinos. Trillions of themare passing through your body everysecond. Why don’t you feel them?Because their probability ofinteracting is so small.
An experiment set up by Ray Davis tolook for neutrinos from the Sun (in theHomestake Mine in South Dakota)found only ~1/2 of the numberexpected (running from 1970 throughthe present)
Have nuclear reactions in the Sunstopped?
Within the last 2 years, it has beenunderstood that there are 3 types ofneutrinos and that the neutrinosproduced in the Sun metamorphizeinto another type (that can’t bedetected) before they reach the Earth.
Whew!
Radioactive Dating We can often use radioactivity to
measure the age of an object(artifact, fossil, etc)
Consider 14C dating◆ cosmic ray interactions in the
upper atmosphere cause nuclearinteractions that produce 14Cfrom 14N
◆ living organisms breathe incarbon dioxide that has both 12Cand the radioactive 14C
◆ so all living creatures have thesame ratio of 14C to 12C(~1.3X10-12)
◆ when the organism dies,however, it no longer absorbscarbon dioxide from the air, andso the ratio of 14C to 12Cdecreases
Can measure therate for the reactionbelow per unit mass,and from it calculatehow long somethinghas been dead◆ 14 14
12C 7N + e- + ν
◆ the greater the ratethe more recently ithas died
Carbon dating
Works on samples fromabout 1 to 25,000 yearsago◆ why not longer?◆ half-life of 14C is 5730
years, so longer than 5half-lives too small afraction of 14C is left (25=32so <1/32nd left)
Examples:◆ Dead Sea Scrolls date to
1950 years ago◆ Iceman dates to 5300
years ago◆ Shroud of Turin to 700
years ago
Radioactivity
Radioactivity can beclassified into 2groups◆ unstable nuclei found
in nature (naturalradioactivity)
◆ nuclei produced in thelab through nuclearreactions (artificialradioactivity)
Four radioactive series shown below. Uranium, Actinium and Thorium are all found in nature.Neptunium is trans-uranic.
Decay chain for Thorium
Start with 232Th◆ half-life for first decay
is ~14 billions years
End with 208Pb
Radiation damage Radiation damage in biological
organisms is primarily due toionization effects in cells◆ normal function of a cell can
be disrupted when highlyreactive ions or radicals areformed as a result of ionizingradiation
◆ damage to a great number ofcells can lead to death
◆ cells which do survive theradiation may becomedefective and cancerous
Can divide radiation damage into2 types◆ somatic (to non-reproductive
cells)◆ genetic (to reproductive cells)
Units of radiation damage◆ rad: that amount of radiation
that deposits .01 J into 1 kg ofabsorbing material
◆ rem is defined as the productof dose in rads and RBE(relative biologicaleffectiveness) factor
Radiation exposures
Low level radiation fromcosmic rays, radioactiverocks, soil, air deliver adose of about 0.13rem/year
Upper limitrecommended bygovernment is 0.5rem/year
Acute whole-body doseof 500 rem results in amortality rate of ~50%
Natural sources of exposure◆ cosmic rays: 14%◆ radon: 58%◆ food: 12%◆ ground: 16%
Equivalent exposure frommedical X-rays◆ chest/teeth/arms and legs: a
few days▲ also equivalent to the
radiation exposure from a 4-hour plane flight
◆ breast, spine, abdomen: afew months
◆ barium enema: a few years
What about exposure from microwave ovens?
E=hc/λ
Nuclear fission Nuclear fission occurs when a
heavy nucleus such as 235U splitsor fissions into 2 smaller nuclei
In such a reaction the total massof the products is less than theoriginal mass of the heavynucleus◆ where does the extra mass go?◆ into kinetic energy of decay
products, about 200 MeV (notjust of academic interest)
Consider a slow neutroninteracting with a 235U nucleus(one possible reaction)
1 235 141 92 1 0n + 92U 56Ba + 36Kr + 30n
235U captures slow-movingneutron
Capture results in formation of236U*; excess energy of thisnucleus causes it to undergoviolent oscillations
236U nucleus becomeselongated
Nucleus splits into 2fragments, emitting severalneutrons in the process
Chain reactionAverage number of neutrons emitted is ~2.5; when chain reactionoccurs fast, it’s a bomb; when reaction occurs slowly and controlledit’s a nuclear reactor
First chain reaction
In 1942, Enrico Fermiand collaborators built anuclear pile underneaththe football stadium andobtained the firstcontrolled nuclear chainreaction
Their measurementsconfirmed that theconstruction of an atomicbomb was a possibility
Enrico Fermi Physicist 1901 - 1954
Nuclear Reactor• in a reactor have control
rods which can absorbneutrons to slow thereaction down
Operating principles