p-nuclear physics 09

A. ATOMIC PHYSICS and QUANTUM EFFECTS 1. PHOTONS and the PHOTOELECTRIC EFFECT 2. WAVE-PARTICLE DUALITY 3. BOHR MODEL and ENERGY LEVELS

B. NUCLEAR PHYSICS 1. RADIOACTIVITY 2. NUCLEAR REACTIONS

IV. MODERN PHYSICS CONTENT OUTLINE

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A. P. PHYSICS SPANGLER 12/18/11

OBJECTIVES for the STUDY of NUCLEAR PHYSICS1. RADIOACTIVITY and HALF-LIFE

a. Understand the significance of half life in radioactive decay so they can:i. Recognize that half-life is independent of the number of nuclei present or of external conditions.ii. Sketch a graph to indicate what fraction of a radioactive sample remains as a function of time, and indicate the half-life on such a graph.iii. Determine, for an isotope of specified half-life, what fraction of the nuclei have decayed after a given time has elapsed.

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PROTON

NEUTRON

Nuclear StructureThe nucleus consists of neutrons and protons, collectively referred to as, nucleons.

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There are approximately 2000 nuclides. Nuclei are made from protons and neutrons and are represented symbolically as:

NUCLIDES

Where: X represents the chemical symbol for the element. A is the atomic mass number, which equals the total number of nucleons in the nucleus. Z is the atomic number, which equals the number of protons in the nucleus.Nuclide mass is in AMU, u 1u=1.661x10-27 Kg

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ISOTOPES of CARBON

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Other Particles

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Nuclide mass is in atomic mass units, u 1 u = 1.661x10-27 Kg = 931.5 MeV

A.M.U.s

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Most nuclei are approximately spherical, with an average radius given by:

Where:A is the mass number r0 is a constant equal to 1.2 x 10-15 m = 1.2 fm 1 fm=1x10-15 mAn atom’s radius is about 10-10m

NUCLEAR RADII

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SNF and the STABLE NUCLEUS

Independent of Charge

Very Strong at Less Than 10-15 meters0 at Greater Distances

All Nuclei greater Than Z=83 Are Not Stable and Spontaneously Decay, Called Radioactivity

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The MASS DEFECT of the NUCLEUS and NUCLEAR BINDING ENERGY

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IE for BINDING ENERGY The Binding Energy of the Helium Nucleus

The most abundant isotope of helium has a He nucleus whose mass is 6.6447 X 10-27 kg. For this nucleus, find (a) the mass defect and (b) the binding energy. The symbol He indicates that the helium nucleus contains Z = 2 protons and N =4 - 2 = 2 neutrons. To obtain the mass defect Δm, we first determine the sum of the individual masses of the separated protons and neutrons. Then we subtract from this sum the mass of the He nucleus. Finally, we use E = (Δm)c2 to calculate the binding energy from the value for m.

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Solution: (a) Using data from Table 31.1, we find that the sum of the individual masses of the nucleons is: Two protons + Two neutrons = 2(1.6726 x 10-27 kg) + 2(1.6749 x 10-27 kg)= 6.6950 x 10-27kg

This value is greater than the mass of the intact He nucleus, and the mass defect is: 6.6950 X 10-27kg - 6.6447 X 10-27kg = 0.0503 X 10-27kg

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(b) The binding energy is:Binding = (m)c2 (0.0503 X 10-27kg)(3X108 m/s)2 = 4.53 X 10-12J energy

Usually, binding energies are expressed in energy units of electron volts instead of joules (1 eV = 1.60 X 10-19J):Binding energy = (4.53X10-12 J)= 2.83X107 eV = 28.3 MeVThe value of 28.3 MeV is more than two million times greater than the energy required to remove an orbital electron from an atom.

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BINDING ENERGY per NUCLEON

None Stable Pass Bi

62 Ni Most Stable

2 Small Nucleus Fusion to 1 Larger

1 Large Fission to 2 Smaller

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RADIOACTIVITY

Radioactive nuclei are generally classified into two groups: 1. Unstable nuclei found in nature, which give rise to what is called natural radioactivity.2. Nuclei produced in the laboratory through nuclear reactions, which exhibit artificial radioactivity.

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The spontaneous emission of radiation by certain nuclei is called radioactivity. Most nuclides are radioactive. There are 3 processes by which a radioactive substance can decay:

1. ALPHA, a decay, in which the emitted particles are He nuclei. 2. BETA, β- decay, in which the emitted particles are electrons. A neutron converts to a proton and an electron.3. GAMMA, γ decay, in which the emitted particles are high-energy photons, called gamma, γ rays.

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Paper

Aluminum

Steel

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ALPHA, α DECAY

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SMOKE DETECTOR

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BETA, β DECAY

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DISINTEGRATION ENERGY

A new element is formed when alpha or beta decay occurs. The changing of one element (parent nucleus) into a new element (daughter nucleus) is called transmutation.The total energy released during alpha decay is called the disintegration energy Q.

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GAMMA, γ DECAY

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GAMMA KNIFE RADIOSURGERY

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The NEUTRINO

1. No Charge

2. Almost Zero Rest Mass3. Interacts Weakly with Matter Making It

Difficult to Detect

Existence Suggested by Pauli in 1930, named by Fermi, Detected in 1950

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The RATE of DECAY and HALF-LIFE

The Law of Radioactive Decay

Radioactive nuclide spontaneously emit a particle, transforming itself in the process into a different nuclide. Radioactive decay provided the first evidence that the laws that govern the subatomic world are statistical.

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Consider, for example, a 1 mg sample of uranium metal. It contains 2.5 X 1018 atoms of the very long-lived radionuclide 238U.

The nuclide of these particular atoms have existed without decaying since they were created, well before the formation of our solar system.

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During any given second only about 12 of the nuclide in our sample will happen to decay by emitting an alpha particle, transforming themselves into nuclide of 234Th.

There is absolutely no way to predict whether any given nucleus in the sample will be among the small number of nuclei that decay during the next second. All have an equal chance.

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Counter Example:Note: Light bulbs (for one example) follow no such exponential decay law. If we life-test 1000 bulbs, we expect that they will all "decay" (that is, burn out) at more or less the same time. The decay of radionuclides follows quite a different law.

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We can express the statistical nature of the decay process by saying that if a radioactive sample contains N radioactive nucilei at some instant, then the number of nuclei, ΔN, that decay in a short time interval Δt is proportional to N.

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where:λ is the decay or disintegration constant, which is different for different isotopes, and has units of 1/sec.

The negative sign in the equation indicates that the number of radioactive nuclei present is decreasing.ΔN/Δt is the rate of decay, called the activity of the isotope is the number of decays per second.

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Where:

No is the number of radioactive nuclei present in the original sample, the number at t = 0 s. N is the number of radioactive nuclei present at future time t e = 2.718

The number of radioactive nuclei present is obtained by integrating the above equation, resulting in:

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Exponential Decay Curve

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The activity can be written as:

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The Sl unit for activity

The Sl unit for activity is the becquerel, Bq, named for Henri Becquerel, the discoverer of radioactivity:1 Bq and is equal to 1 decay/secAn older unit is the Curie, where 1Ci = 3.7x1010Bq

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An example of the use of these units is the following statement: "The activity of spent reactor fuel rod #5658 on January 15, 1997, was 3.5 x 1015 Bq (= 9.5 x 104 Ci) Thus, on that day 3.5 x 1015 radioactive nuclei in the rod decayed each second. The identities of the radionuclides in the fuel rod, their disintegration constants λ, and the types of radiation they emit have no bearing on this measure of activity.

IE for Units of Activity

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HALF-LIFE, T1/2

Another useful parameter for characterizing the radioactive decay of any isotope is its half-life. The half-life, T1/2 of an isotope is the time required for half of the radioactive nuclei present in the sample to decay.

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The relationship between the half-life and the decay constant can be found by setting N=N0/2 and t= T1/2 in the equation N=N0e- λt and solving for T1/2

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REMAINING NUCLEI versus HALF-LIVES

The graph below shows the number of undecayed nuclei (parent nuclei) present as a function of time, where the time is expressed in terms of half lives. This type of curve is known as an EXPONENTIAL DECAY CURVE.

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For problems related to half life, decay constant and radioactive decay.If either the half life or decay constant is given, use T1/2 = .693/λ

to determine either the half life or decay constant.

Use the law of radioactive decay N = No e-λt

to determine the number of nuclei remaining after a certain time has passed.

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ILLUSTRATIVE EXAMPLE for radioactive decay. A 2.00 microgram sample of pure 49Cr is to be used in a laboratory experiment. The half life of the isotope is 42 min. Determine the: a. Decay constant of the isotope b. Number of original nuclei remaining after 2.80 hours.a1. Determine the half life in seconds.a2. Determine the decay constant for this element.b1. Determine the number of half lives that have passed in 2.8 h.b2. Determine the number of moles of the original sample that is present after 4 half lives.b3. Determine the number of nuclei of Cr 49 present after 2.8 h.

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RADIOACTIVE DATING

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RADIOACTIVE DECAY SERIES

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RADIATIONDETECTORS

Geiger Counter

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Scintillation Counter

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p-nuclear physics 09

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