chapter 43. nuclear · pdf filenuclear physics the nucleus of the atom is extremely remote...

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

Chapter 43. Nuclear Physics The nucleus of the atom is extremely remote from our everyday experience. However, nuclear physics part of our modern technology, for example, nuclear power, nuclear medicine and nuclear waste. Chapter Goal: To understand the physics of the nucleus and some of the applications of nuclear physics.


Topics: •  Nuclear Structure •  Nuclear Stability •  The Strong Force •  The Shell Model •  Radiation and Radioactivity •  Nuclear Decay Mechanisms •  Biological Applications of Nuclear Physics


The nucleus is composed of two types of particles: protons and neutrons. Together, these are referred to as nucleons. The number of protons Z is the element’s atomic number. The mass number A is defined to be A = Z + N where N is the neutron number. The mass number is the total number of nucleons in a nucleus.


The conversion to SI units is 1 u = 1.6605 × 10−27 kg. The atomic mass unit can be written 1 u = 931.49 MeV/c2. It may seem unusual, but the units MeV/c2 are units of mass.

Atomic masses are specified in terms of the atomic mass unit u, defined such that the atomic mass of the isotope 12C is exactly 12 u.


•  The stable nuclei cluster very close to the curve called the line of stability.

•  There are no stable nuclei with Z > 83 (bismuth).

• Unstable nuclei are in bands along both sides of the line of stability.

•  The lightest elements, with Z < 16, are stable when N ≈ Z.

• As Z increases, the number of neutrons needed for stability grows increasingly larger than the number of protons.


•  The binding energies of nuclei are tens or hundreds of MeV, energies large enough that their mass equivalent is not negligible.

• Consider a nucleus with mass mnuc. It is found experimentally that mnuc is less than the total mass of the Z protons and N neutrons that form the nucleus.

•  Scientists measure atomic masses, not nuclear masses. The atomic mass matom is mnuc plus the mass Zme of Z orbiting electrons. (Neglect electronic binding energy.)

•  The nuclear binding energy is then

where all three masses are in atomic mass units.


QUESTION:


1. It is an attractive force between any two nucleons.

2. It does not act on electrons. 3. It is a short-range force,

acting only over nuclear distances.

4. Over the range where it acts, it is stronger than the electrostatic force that tries to push two protons apart.

The strong force has four important properties:


•  The shell model of the nucleus, using multielectron atoms as an analogy, was proposed in 1949 by Maria Goeppert-Mayer.

•  The shell model considers each nucleon to move independently with an average potential energy due to the strong force of all the other nucleons.

•  The depth of the neutron’s potential-energy well is ≈50 MeV for all nuclei.

•  For protons, the positive electrostatic potential energy “lifts” the potential energy well.

• Outside the nucleus, a proton has a positive potential energy which decreases slowly with increasing distance.


Let r be the probability that one particular nucleus will decay in the next 1 s by emitting an alpha or beta particle or a gamma-ray photon. Notice that r, which is called the decay rate, has units s–1. If there are N independent nuclei, the number of nuclei expected to decay during Δt is

The rate of change in the number of radioactive nuclei depends both on the decay rate and on the number of radioactive nuclei present:


The number of remaining nuclei N at time t is

where we define the time constant τ = 1/r. We can write this equation in terms of the half-life t1/2 as

Thus N = N0/2 at t = t1/2, N = N0/4 at t = 2t1/2, N = N0/8 at t = 3t1/2, and so on. No matter how many nuclei there are, the number decays by half during the next half-life.


QUESTIONS:


The activity R of a radioactive sample is the number of decays per second. This is simply the absolute value of dN/dt, or

where R0 = rN0 is the activity at t = 0. The SI unit of activity is the becquerel Bq, defined as 1 Bq = 1 decay/s or 1 s–1. An older unit of activity, but one that continues in widespread use, is the curie Ci. The conversion factor is 1 Ci = 3.7 × 1010 Bq.


QUESTION:


You are what you eat. Literally!


An alpha particle is a 4He nucleus, a strongly bound system of two protons and two neutrons. An unstable nucleus that ejects an alpha particle will lose two protons and two neutrons, so we can write the decay as

The original nucleus X is called the parent nucleus, and the decay-product nucleus Y is the daughter nucleus. The energy released in an alpha decay, essentially all of which goes into the alpha particle’s kinetic energy, is


QUESTION:


•  The absorbed dose of radiation is the energy of ionizing radiation absorbed per kilogram of tissue. The SI unit of absorbed dose is the gray Gy. It is defined as 1 Gy = 1.00 J/kg of absorbed energy.

• Biophysicists have found that a 1 Gy dose of gamma rays and a 1 Gy dose of alpha particles have different biological consequences. To account for such differences, the relative biological effectiveness (RBE) is defined as the biological effect of a given dose relative to the biological effect of an equal dose of x rays.


•  The product of the absorbed dose with the RBE is called the dose equivalent.

• Dose equivalent is measured in sieverts Sv. dose equivalent in Sv = absorbed dose in Gy × RBE

• An older but still widely used unit for dose equivalent is the rem, defined as 1 rem = 0.010 Sv. Small radiation doses are measured in millisievert (mSv) or millirem (mrem).


QUESTION:

chapter 43. nuclear · pdf filenuclear physics the nucleus of the atom is extremely remote...

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