ib assessment statements topic 13.2, nuclear physics 13.2.1.explain how the radii of nuclei may be...

DEVIL PHYSICSTHE BADDEST CLASS ON

CAMPUSIB PHYSICS

TSOKOS LESSON 6-6NUCLEAR PHYSICS

IB Assessment Statements

Topic 13.2, Nuclear Physics13.2.1. Explain how the radii of nuclei

may be estimated from charged particle scattering experiments.

13.2.2. Describe how the masses of nuclei may be determined using a Bainbridge mass spectrometer.

13.2.3. Describe one piece of evidence for the existence of nuclear energy levels.

Topic 13.2, Nuclear Physics13.2.4. Describe β+ decay, including

the existence of the neutrino.13.2.5. State the radioactive decay

law as an exponential function and define the decay constant.

13.2.6. Derive the relationship between decay constant and half-life.

Topic 13.2, Nuclear Physics13.2.7. Outline methods for

measuring the half-life of an isotope.

13.2.8. Solve problems involving radioactive half-life.

Objectives

Solve problems of closest approach using the law of conservation of energy and appreciate that nuclei have well-defined radii

Describe a mass spectrometer and its implications for isotope existence

State theoretical arguments that have been used to postulate the existence of the neutrino

Objectives

State the radioactive decay law,

State the meaning of half-life and decay constant and derive the relationship between them

Objectives

Appreciate that the decay constant is the probability of decay per unit time

Understand that the initial activity of a sample is,

Obtain short and long half-lives from experimental data

Objectives

Solve problems with activities and the radioactive decay law

Scattering Experiments and Distance of Closest Approach An alpha particle of charge q=+2e is

fired head-on at a nucleus The particle’s total energy is kinetic,

Scattering Experiments and Distance of Closest Approach The particle is repelled by the

positive charge of the nucleus

Scattering Experiments and Distance of Closest Approach When the particle stops, all of its

kinetic energy has been converted into potential energy

Scattering Experiments and Distance of Closest Approach When the particle stops, all of its

kinetic energy has been converted into potential energy

Scattering Experiments and Distance of Closest Approach As kinetic energy of the alpha

particle increases, distance decreases until the nuclear radius is reached

Scattering Experiments and Distance of Closest Approach Rutherford Scattering

http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html

Closest Approach to Nucleus http://hyperphysics.phy-astr.gsu.edu/hbase/h

frame.html Nuclear Radius Relationship

http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html

Scattering Experiments and Distance of Closest Approach Further experiments have been able

to refine the estimates for nuclear radii to be

mxxAR 1531 102.1

Mass Spectrometer

Positive ions pass through a combination magnetic and electric field so that only ones with a certain velocity will pass through S2

Mass Spectrometer

vmevBF

2 The positive ions then enter a third magnetic field which causes the ion to take a circular path, the radius of which is determined by its mass.

Mass Spectrometer Given the same

velocity, particles with a greater mass will have greater kinetic energy and thus a larger radius of curvature

Existence of isotopes was found using a mass spectrometer

Beta Decay and the Neutrino Decay of a neutron

Decays into a proton, electron, and an antineutrino

This happens to free neutrons outside the nucleus because neutrons have greater mass than protons

Half-life is about 11 minutes

evepn 00

Beta Decay and the Neutrino Decay of a proton

Decays into a neutron with the emission of a positron (anti-particle of an electron) and a neutrino

Decay occurs inside the nucleus where binding energy makes up for the mass difference

Not a split, but a disappearance and reformation

evenp 00

Beta Decay and the Neutrino Presence of neutrinos

predicted because the mass of a neutron is greater than the sum of the mass of a proton and electron

evepn 00

evenp 00

Beta Decay and the Neutrino In other decays, this

mass difference showed up in kinetic energy of the particles

evepn 00

evenp 00

Beta Decay and the Neutrino Absence of the kinetic

energy led to experiments that uncovered the neutrino (little neutral one) in 1953

evepn 00

evenp 00

Beta Decay and the Neutrino Electron Capture

A proton inside the nucleus captures an electron and turns into a neutron and neutrino

This is the process occurring in neutron stars

Huge pressure inside the star drives electrons into protons, turning them into neutrons

evnep 00

Beta Decay and the Neutrino Examples of Beta

Decayevepn 0

10 evenp 0

11 evnep 0

Nuclear Energy Levels

The nucleus, like the atom, exists in discrete energy levels

Main evidence is that alpha particles and gamma ray photons are emitted in discrete energy levels during decays

In beta decays, the electrons have a continuous range of energies

Nuclear energy levels of

Shown is a gamma decay (release of a photon) with energy

Mg2412

MeV87.337.124.5

Two decays of plutonium into uranium with release of an alpha particle

4223892

24294 UPu

Radioactive Decay Law

The number of nuclei that will decay per second is proportional to the number of atoms present that have not yet decayed

λ is a constant known as the decay constant

Represents the probability of decay per unit time

The number of undecayed nuclei N at any given time in relation to the original number of undecayed nuclei N0 is given by the equation,

The decay rate is exponential

teNN 0

The derivation to the right gives the relationship between half-life and decay rate

The number of decays per second is called the activity,

The initial activity is

The decay constant represents the probability of decay per unit time

yprobabilit

dNyprobabilit

Σary Review

Can you solve problems of closest approach using the law of conservation of energy and appreciate that nuclei have well-defined radii?

Can you describe a mass spectrometer and its implications for isotope existence?

Can you state theoretical arguments that have been used to postulate the existence of the neutrino?

Σary Review

Can you state the radioactive decay law,

? Can you state the meaning of half-life

and decay constant and derive the relationship between them?

Σary Review

Do you appreciate that the decay constant is the probability of decay per unit time?

Do you understand that the initial activity of a sample is,

? Can you obtain short and long half-

lives from experimental data?

Σary Review

Can you solve problems with activities and the radioactive decay law?