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What’s Inside… • In this module, we discuss the properties and structures of atomic nucleus. We start by describing the basic properties of the nuclei and then the discussion of nuclear forces and binding energy, and the phenomenon of radioactivity. After that we tackle about nuclear reaction and the various processes by which nuclear decay. By the way, we’ll also talk about fusion reaction. ^^
Table of Contents…. • Introductions……………….........................................….1-3 • Pre-Test……………………………...................................4-13 • The Nucleus……………………………………………......14-19 • Quiz 1………………………………………………………..20-25 • Binding energy and Nuclear stability……………………..26-33 • Quiz 2………………………………………………………..34-38 • Radioactive Decay and Half-life…………………………..39-57 • Quiz 3…………………………………………………….….58-63 • Nuclear Reaction…………………………………………...64-70 • Quiz 4………………………………………………………..71-75 • Fusion Reaction…………………………………………….76-85 • Quiz 5……………………………………………………......86-87 • Post test……………………………………………………..88-99 • Answers……………………………………………………..100-107
Pre-test Let’s see what you’ve got….
Which of the following is not an example of ionizing radiation? a. alpha b. beta c. gamma d. x-ray e. microwave
What is the atomic number of ? • In beta decay, β–, an electron is emitted along with the daughter nucleus. What is the other particle emitted? • emits a gamma ray. The resulting nucleus is
Uranium-236 fissions into and another nucleus with the release of three neutrons. What is the atomic mass number of the second nucleus? • decays by alpha decay. The resulting isotope is
An amateur scientist tells you he has a stable atom of , why is that unlikely? a. No atoms are stable b. Amateur scientists don't know anything. c. There are no stable nuclei with more than 83 protons. d. Male scientists can't be trusted.
An alpha particle is a. an electron b. a positron c. a Helium nucleus d. the first one to come out
A beta particle is a. an electron b. a positron c. a Helium nucleus d. the second to come out
A gamma ray is a. an electron b. a Helium nucleus c. an energetic ray of invisible light d. the 3rd to come out
A hypothetical stable nucleus with 89 protons and 129 neutrons must have a mass of less than __ u (to the nearest ten thousandth of a u).
element has the same Z values but differ in N and A values • What is the mass of to the nearest u? • The strongest force in nature • who first observe nuclear reactions?
The Nucleus Chapter I
We describe the atomic nucleus using the following quantities….. • Atomic Number • equal to the number of proton • Neutron Number • equal to the number of neutron • Mass Number • equal to the number of nucleon ↖[proton + neutron]
Element Mass Number NeutronNumber Atomic Number In representing the nuclei we use this symbol: A X N Z isotones are elements with the same number of neutrons N which are relatively rare fortunately, neutron number usage is obsolete so it’s not necessary to include that in writing the element Isobars are elements with the same mass number A but different Z The isotopes of an element has the same Z values but differ in N and A values
The Mass and Charge Coloumb (c) Unified Atomic Mass Unit (u), u ≈ 1.66053886 × 10−27 kg ≈ 931.49 MeV/c2
1.2 fm Mass Number The Size and Structure of the Nuclei • The radius of a nucleon is of the order of 1 fermi = 10-15 m • The nuclear radius can be approximated by:
The nucleus is viewed as a closely packed collection of protons and neutrons • The volume of the nucleus (assumed to be spherical) is directly proportional to the total numbers of nucleon • This suggest that all nuclei have nearly the same density
1. The mass number of a nuclide refers to the sum of the masses of _____. a. the protons and neutrons in the nucleus b. the protons in the nucleus c. the electrons in the nucleus d. the neutrons in the nucleus Quiz # 1
Quiz # 1 2. Which one of the nuclides shown below is an isotope of a. b. c. d.
Quiz # 1 3. Which one of the nuclides shown below has the same number of neutrons as the nuclide a. b. c. d.
Quiz # 1 3. Isotones are elements with…. a. the same mass number A but different Z b. the same Z values but differ in N and A values c. the same number of N but differ in Z and A values d. the same number of A,N and Z values
Quiz # 1 5. It is the number of protons and neutrons a. nuclide b. neutrino c. nucleon d. nucleotides
Binding Energy and Nuclear Stability Chapter II
Binding Energy and Nuclear Stability • The nuclei are stable because of the strong nuclear force • It is the competition between the repulsive electrostatic forces and the attractive strong nuclear forces that determines whether a given nucleus is stable
Nuclear force • a very short range (about 2 fm) attractive force that acts between all nuclear particles • it acts between pairs of neutrons and between neutrons and protons • The strongest force in nature • Independent of the charge of interactive nucleons
Neutron Count (N) Proton Count (Z) Here, we plotted N vs. Z for a number of stable nuclei (black dots) This is the line of stability • light nuclei are most stable if they contain an equal number of Z and N • heavy nuclei (Z>20) are more stable if Z is greater than N • Elements which have Z>83 doesn’t have stable nuclei N=Z
Mass of proton Mass of neutron Mass of the nucleus • The mass of a nucleus is always less than the sum of the masses of its constituent nucleons. • The difference is known as mass defect: • Δm is the mass that would be transformed into energy, if a nucleus is to be constructed by the necessary number of protons and neutrons.
The energy equivalent of the mass defect is called the binding energyof the nucleus • Binding energy (Eb) • energy needed to split a nucleus into its components • energy needed to bind the nuclei *the masses are all expressed in atomic mass units
BINDING ENERGY PER NUCLEON (MeV) MASS NUMBER Binding energy of the nucleon vs. mass number for nuclei that lie along the line of stability • Nuclei having A > or < 60 are not as strongly bound as those near in the middle periodic table • as the atomic mass number increases, the binding energy per nucleon decreases for A > 60 • binding energy per nucleon is approximately constant at around 8 MeV per nucleon for all nuclei with A>50 Region w/ greatest stability
The lightest nuclei, like deuterium and tritium, have the smallest binding energy • Iron-56 is the most tightly bound nucleus • The heaviest nuclei are not bound as loosely as the lightest nuclei, but are bound less tightly than those with A =60 • Fusion is the process of bringing together two light nuclei to form a more tightly bound heavier nucleus while releasing a particle...typically a neutron. • Fission is a process in which a heavy nucleus fragments into two medium nuclei with the release of two or more neutrons
Quiz # 2 1-2. Most stable nuclei with small atomic numbers have ____, while those with large atomic numbers have ____. a. more neutrons than protons b. more protons than neutrons c. equal numbers of neutrons and protons d. equal numbers of protons and electrons
Quiz # 2 3. Which nuclei have the largest average binding energies per nucleon? a. A < 20 b. 30 <A< 100 c. A>200 d. they are all the same
Quiz # 2 4. Which of the following is not true? a. nuclides located in the middle of the periodic table have greater stability than the others b. as the atomic mass number increases, the binding energy per nucleon decreases for A > 60 c. binding energy per nucleon is approximately constant at around 8 MeV per nucleon for all nuclei d. Iron-56 is the most tightly bound nucleus
Quiz # 2 5. Nuclear fission a. is the splitting of heavy nuclei into lighter ones b. is the combining of light nuclei to form heavier ones. c. results from a series of alpha decays. d. releases much less energy per atom than a chemical process.
Radioactive Decay and Half Life Chapter III
Radioactivity - the process of spontaneous emission of radiation • Radioactive (unstable) nuclei decay if there is an energetically more favorable condition that it is trying to reach
Radioactive Decays • Change into another element:[XY+decay particle(s)] • α-decay: emits 4He nucleus from unstable nucleus • β-decay: emission of electron or positron (positively charged electron) from unstable nucleus • Spontaneous fission: the radiocative nucleus brake into so called “fission fragments” • An another decay mode (within the nucleus): [X* X + γ’s] • γ-decay: De-excitation from 1 excited state to a bound state (or less excited one...)
α β γ PAPER ALUMINUM LEAD
The rate at which a particular decay process occur in a radioactive sample is proportional to the number of the radioactive nuclei present (the ones that haven’t decayed yet…) The rate of change in N (# of radioactive nuclei present) is….. Decay Constant -the probability of decay per nucleus per second The number of radioactive nuclei at t=0 * The minus sign indicates that N decreases in time
The decay rate which is the number of decays per second can be obtained by differentiating the latter equation (rate of change) with respect to time. • The decay rate R of a sample is often referred to as it’s activity
Half-life • The time it takes half of a given number of radioactive nuclei to decay • This is a convenient relating half-life to decay constant • The SI unit of activity is Becquerel (Bq) • 1 Bq=1decay/s • Another frequently used unit is Curie (Ci) • 1 Ci=3.7x1010 decay/s
Number of half lives Total time The amount of remaining nuclei Amount of nuclei at t=0 Time per half life • The half life formula is • To compute for n
Alpha Decay • When a nucleus emits an alpha particle it looses 2 protons and 2 neutrons • N decreases by 2 • Z decreases by 2 • A decreases by 4 • Symbolically: • X is call the parent nucleus • Y is called the daughter nucleus
Example • Decay of 226Ra • Half life for this decay is 1600 years • Excess mass is converted into kinetic energy • Momentum of two particles is equal and opposite
Beta Decay - Electron Energy • The energy released in the decay process should almost all go to the kinetic energy of the electron • Experiments show that few electrons had his amount of kinetic energy • To account for the “missing” energy, in 1930 Pauli proposed the existence of another particle • Enrico Fermi later named this particle the neutrino • Properties of neutrino • 0 charge • Mass much smaller than electron, probably not 0 • Spin of ½ • Very weak interaction with matter
