If there is a WS for a Sim in NUCLEAR , Then it should be in the student’s booklets.

Quantum and Nuclear Physics (B)

Mr. KlapholzShaker Heights

High School

http://www.sccscience.com/NEWSITE/index3.htm

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.

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?

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.

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

Mass Spectrometer

http://www.mhhe.com/physsci/chemistry/carey/student/olc/ch13ms.html

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!

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.

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.

Velocity Selector

http://commons.wikimedia.org/wiki/File:Velocity_selector.svg

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.

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…

Mass Spectrometer

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.

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…

Number of as vs. kinetic energy

http://www.e12.physik.tu-muenchen.de/~gernhaus/projects/gassipl/gassidok.html

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….

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.

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’

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

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)

All Radioactive Decay shows this pattern: N vs. T

http://www.kgs.ku.edu/Extension/geotopics/earth_age.html

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).

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

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.

Half life (1 of 2)

http://www.tpub.com/content/doe/h1019v1/css/h1019v1_57.htm

Half Life (2 of 2)

http://www.avon-chemistry.com/atom_lecture.html

Equation fits the graph: N = N0e-lt

http://www.tpub.com/content/doe/h1019v1/css/h1019v1_57.htm

Math and Decay (1 of 2)

N = N0e-lt

A = l NA = l N0e-lt

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