If there is a WS for a Sim in NUCLEAR , Then it should be in the student’s booklets.
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Transcript of If there is a WS for a Sim in NUCLEAR , Then it should be in the student’s booklets.
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If there is a WS for a Sim in NUCLEAR , Then it should be in the student’s booklets.
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Quantum and Nuclear Physics (B)
Mr. KlapholzShaker Heights
High School
http://www.sccscience.com/NEWSITE/index3.htm
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Warm up: How high does it go?
• If you throw an object straight up, how high does it go?
• You give it a certain speed when you throw it: v.• That’s equivalent to giving it a specific kinetic
energy: 1/2mv2.• How high does it go? One way to answer is to say
that at the top, all of the kinetic energy has been changed to gravitational potential energy.
1/2mv2 = mgh• Solve for h, and you’re done.
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Nuclear Version: How close does it go? (dc)
http://www.schoolphysics.co.uk/age16-19/glance/Nuclear%20physics/Distance_of_closest_approach/index.html?PHPSESSID=ef06d84a72e17bf26a26bb6d0e0051e5
Also, why can’t the alpha get allthe way to the nucleus?
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Nuclear Version: How close does it go? (dc)The alpha particle has a certain amount of energy in the beginning: 1/2mv2.At its closest point, all of the kinetic energy has been changed to electrical potential energy.
1/2mv2 = kq1q2/ rIn general, the r stands for the distance between the charged objects, but in this equation it will actually be our best estimate of the radius of the nucleus.Solve for r, and you’re done.
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Overview of The Mass Spectrometer• This device reveals that atoms of the same
element have different masses.• We call these variations: isotopes of the element.• The device has two main parts: – Velocity selector – Mass detector
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Mass Spectrometer
http://www.mhhe.com/physsci/chemistry/carey/student/olc/ch13ms.html
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Mass Spectrometer 1 - Ionization(There is more than one way to start the beam.)
• A source of atoms is in a box with a high voltage across it. Some of the atoms lose an electron due to the high voltage; these atoms are ‘ionized’.
• None of the ions are negative. The atoms that lose an electron are positively charged, and they stream toward the negative plate.
• There is a hole (or slit)in the plate, so some of the ions just shoot right through. Some of them will get to go into the Mass Spectrometer!
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Mass Spectrometer 2 - Collimation
• The atoms that have left the ionization chamber are fanning out.
• To get a beam of ions that are more nearly alike, there are more barriers in the path, but each has a hole.
• Think of this as a direction selector.
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Mass Spectrometer 3 – Velocity Selector
• The ions enter a region with a magnetic field (B) and an electric field (E). The fields are perpendicular to each other.
• The magnetic force (evB) on the ions is opposite in direction to the electric force (eE) on the ions.
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Velocity Selector
http://commons.wikimedia.org/wiki/File:Velocity_selector.svg
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Mass Spectrometer 3 – Velocity Selector
• If an ion is moving very fast, then evB > eE. • If an ion is moving slowly, then evB < eE. • If an ion is not deflected, then the force down
equals the force up: evB = eE vB = E v = E/B
• The only ions that make it through the velocity selector without bending out of the beam, are the ones with velocity: E/B.
• The values of B and E can be adjusted to select any velocity.
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Mass Spectrometer 4 – Mass Separator• Now the beam is made of ions all going in about the
same direction and going about the same (known) speed. Let’s bend them.
• The ions enter a magnetic field (B2) that is different from the first magnetic field.
• The field bends the particles into a circular path. The radius of the circle is easy to measure, and from that we can distinguish one mass from another because low-mass ions bend more.
• If you put a hole at the location of a specific isotope, then the Mass Spectrometer becomes a source of a specific isotope…
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Mass Spectrometer
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Quantization of marbles
• Imaging putting a bag with a lot of marbles on a balance.
• If you take out any number of marbles at a time, the changes in mass would always be multiples of the mass of one marble.
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Quantization of the energy of the nucleus
• The nucleus has energy levels.• Evidence for this is in alpha emission:
(42a = 4
2He)• When a large nucleus emits alpha particles,
the alphas have only specific energies…
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Number of as vs. kinetic energy
http://www.e12.physik.tu-muenchen.de/~gernhaus/projects/gassipl/gassidok.html
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Energy and Momentum seemed to not be conserved in Beta (b) decay.
• Some physicists thought that energy and momentum might not be conserved in all cases (a creative idea that did fit the data).
• Wolfgang Pauli and Enrico Fermi trusted the conservation laws to such a degree that they predicted the existence of a new particle that had just the right properties to agree with the conservation laws….
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The Neutrino (n)
• For it all to work the neutrino needed to have some fairly bizarre properties:
• Charge: neutral• Mass: ultra low, or zero• Speed: ultra fast (maybe even light speed)• Interaction with matter: none, or very little• 5 x 1013 pass through you every second.
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Antimatter Data
• Every particle of matter has a corresponding anti–matter particle.
• The anti-particle has the opposite charge, but the same mass.
• Examples:– proton and antiproton: p and p’– electron and antielectron: e and e’
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Negative Beta (b) decay
n p+ + b- + n’ 14
6C 147N + 0
-1b + n’
Notice that:the betas are negative (they are matter; they are electrons)the neutrinos are anti-matter
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Positive Beta (b) decay
p+ n + b+ + n 11
6C 115N + 0
+1b + n
Notice that:the betas are positive (the anti-matter particle to the electron)the neutrinos are matter (not anti-matter)
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All Radioactive Decay shows this pattern: N vs. T
http://www.kgs.ku.edu/Extension/geotopics/earth_age.html
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Decay Activity (A)• A is the “activity” of an isotope (units: Becquerel
or Bq or Hz or s-1)• A = the number of disintegrations per second.
A = - DN / Dt• N: Number of original nuclei.• DN: Decrease in the number of original nuclei.
This quantity is negative because the number of nuclei keeps decreasing. (Ex.: 990 – 1000 = -10).
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Rate of Decay• The greater the number of undisintegrated nuclei,
the more disintegrate each second. (The greater the population, the greater the number of deaths per day.) A is proportional to N. The fewer nuclei that remain, the slower the decay rate.
http://www.kgs.ku.edu/Extension/geotopics/earth_age.html
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The Decay constant (l)A is proportional to N.
A a NA = l N
Units of l : s-1 ! The decay constant (l ) is the probability that a single nucleus will decay in one second.
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Half life (1 of 2)
http://www.tpub.com/content/doe/h1019v1/css/h1019v1_57.htm
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Half Life (2 of 2)
http://www.avon-chemistry.com/atom_lecture.html
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Equation fits the graph: N = N0e-lt
http://www.tpub.com/content/doe/h1019v1/css/h1019v1_57.htm
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Math and Decay (1 of 2)
N = N0e-lt
A = l NA = l N0e-lt
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Math and Decay (2 of 2)Learn this proof (it is in the syllabus)
N = N0e-lt
N / N0 = e-lt If t = T½ then N = ?
If t = T½ then N = N0 / 2 (N0/2) / N0 = e-lT½
1 / 2 = e-lT½ 2 = e+lT½
ln(2) = lT½ ln(2) / l = T½