Assignments Day One: (31.1 – 31.3 Mass Defect/BE) Focus p 982 #1,2,6 Problems p 983 #1-5, 11-13, 15, 18 Day Two: (31.4 – 31.8 Radioactivity) Check: Focus: Problems:. Underwater Nuclear Test I. Underwater Nuclear Test II. Chapter 31.
Day One: (31.1 – 31.3 Mass Defect/BE)
Focus p 982 #1,2,6
Problems p 983 #1-5, 11-13, 15, 18
Day Two: (31.4 – 31.8 Radioactivity)
Underwater Nuclear Test I
Underwater Nuclear Test II
Nuclear Physics and Radioactivity
The classic model of an atom consists of a nucleus (with protons and neutrons), and a set of outer shells/orbitals of electrons.
In an “electrically neutral” atom, the number of protons is balanced by an equal number of electrons.
Because they are found in the nucleus, protons and neutrons are collectively called “Nucleons”
Periodic Table of the Elements
(the number of protons in the nucleus). “Z”
(the mass of the element – mostly due to the # of protons plus the # of neutrons in the nucleus). Also called the nucleon number. “A”
Periodic Table of the Elements
Be aware that the atomic mass is ABOVE the atomic number when writing atomic equations!
Name: CarbonSymbol: CAtomic Number: 6Atomic Mass: 12.0107 amu
On a mini-whiteboard, write the chemical symbol for Carbon, including the mass number and atomic number. For this example, use an atomic mass of 12 amu.
What’s an “amu”? (also called a Dalton)
An atomic mass unit. It is abbreviated as either ‘amu’ or ‘u’ or ‘Da’.
ONE amu is approximately equal to the mass of a single nucleon.
Each proton and neutron has approximately ONE amu.
An amu is defined as 1/12th the mass of a neutral, grounded carbon atom.
Because nuclear particles are so ‘light’, using kilograms just doesn’t make sense.
Nuclei that contain the same number of protons but a different
number of neutrons are known as isotopes. Because each isotope has a different number of neutrons, each isotope has a different mass.
Carbon (C) has 16 known isotopes, from 8C to 22C.
Carbon-8 has a mass of 8 amu. Carbon-22 has a mass of 22 amu.
Of these isotopes, only two are stable: 12C and 13C.
The longest-lived radioisotope is 14C with a half-life of 5,700 years. This is the only carbon radioisotope found in nature. Averaging over natural abundances, the standard atomic mass for Carbon is 12.0107(8) ubut it is aften approximated as just ‘12’ u.
About 98.8% of the Carbon on earth is Carbon-12.
About 1.1% of the Carbon on earth is Carbon-13.
For each ‘particle’ to the right, find the:
# of protons,
Guess the type of particle for the bottom two.
a) How many neutrons are there in a Carbon-12 atom?
b) How many neutrons are there in a Carbon-13 atom?
c) How many neutrons are there in a Bismuth-209 atom?
d) How many protons in a Carbon-22?
e) How many protons in a Bismuth-209?
The nuclear radius depends upon the atomic mass. The more nucleons, the greater the radius. The formula below gives the radius in meters:
Aluminum has 13 protons (Z) and an atomic mass of A = 27.
Find the nuclear radius in meters.
Lead and oxygen are different atoms and the density of solid lead is much greater than gaseous oxygen. (Duh).
Recall that density = mass/volume.
If we define m = the mass of each nucleon (a proton or a neutron, then:
the total mass of an atom ≈ A * m,
A is the number of protons and
m is the mass of each nucleon.
Use this information to write a general density equation for an atomic nucleus.
Then, decide whether the density of the nucleus in a lead atom is greater than, approximately equal to, or less than that of an oxygen atom.
Solution, next slide…
Conclusion: The nuclear density is NOT dependent upon the atomic number. Almost all atoms have about the SAME nuclear density!
Note: Density is NOT the same as volume! The nuclear volume does increase, but not the density.
A = atomic weight (“All” the weight)
Z = atomic number (# of protons)
Atomic mass units are ‘amu’ or ‘u’ or ‘Da’.
The nuclear radius is approximately:
r ≈ (1.2 x 10-15)A1/3
And, the density of the nucleus is pretty much constant for ALL atoms!
Summary so far
(we’re not done for the day just yet… interesting stuff still to come!)
In particle physics, the electroweak interaction is the unified description of electromagnetism and the weak interaction. Although these two forces appear very different at everyday low energies, above the unification energy, (about 100 GeV), they merge into a single electroweak force. This occurred when the universe was hot enough (approximately 1015 K) - a temperature exceeded until shortly after the Big Bang).
The mutual repulsion of the protons
tends to push the nucleus apart. What
then, holds the nucleus together?
The strong nuclear force.
The strong nuclear force is NOT dependent upon electric charge. For a given separation distance, the attraction is about equal for pairs of
proton-proton proton-neutron neutron-neutron
It is very strong at distances < m.
(Notice this is the order of magnitude of a nuclear radius!).
It is almost zero at larger distances.
While the strong nuclear force decays quickly with distance, the electric force decays gradually. We say the electric force has a long ‘range of action’.
A nucleon only attracts its nearest neighbors through the strong force. Notice that, due to the electromagnetic force, a proton also repels all other protons at the same time… it is a ‘tug-o-war’ of forces.
All nuclei with > 83 protons are unstable and decay. Their nuclear radius is just too large for the strong force… the electromagnetic force ‘wins’. Bismuth has an atomic number of 83. It is the largest of the stable elements. Notice that it has 126 neutrons. There is a reason for this!
31.2 The Strong Nuclear Force and the Stability of the Nucleus
As nuclei get larger, more
neutrons are required for
They create a “buffer space”… spreading out the protons and decreasing their mutual repulsion. But at the same time, the more nucleons present, the greater the strong force.
The neutrons act like glue
without adding more repulsive
force. They are often referred to as nuclear glue. They are NOT gluons – a different type of elementary particle!
Mass defect & Binding energy
Mass defect & binding energy
Nuclear Binding Energy:
The amount of energy needed to pull apart nuclei. The more stable the nucleus, the more energy is needed. So, the binding energy is greater.
The binding energy, E, appears as extra mass when protons and neutrons are separated.
The mass is converted into energy!
After fusing into a nucleus, the same nucleons now have ‘less mass’!
The nucleons have a certain ‘total mass’ before combining.
Mass defect & binding energy
The difference between the mass of a nucleus and the sum of the masses of the nucleons of which it is composed is called the mass defect.
We must be good at calculating it! Why?
Because we care about energy. And energy and mass are related by
where E is the binding energy, m is the mass defect, and c is the speed of light in a vacuum. If we calculate a change in mass (the mass defect), we can determine the change in energy.
Useful Constants & Conversions:
Speed of light in a vacuum c = 3 x 108 m/s
1.0 AMU = 1.6605 x 10-27 kg = 931.5 MeV
1 electron volt = 1.60217646 × 10-19 joules
Under certain conditions, an electron has a given amount of energy equivalent to 1.6 x 10-19 Joules. This amount of Energy is called an electron-volt, symbol eV.
Three things need to be known to calculate the mass defect:
the actual mass of the nucleus,
the composition of the nucleus (# of protons and neutrons),
the masses of a proton and of a neutron.
To calculate the mass defect:
add up the masses of each proton and neutron that make up the nucleus
subtract the actual mass of the nucleus to obtain the mass defect.
Example: Find the mass defect of a copper-63 nucleus if the actual mass of a copper-63 nucleus is 62.91367 amu.
Step One: Find the composition of the copper-63 nucleus and determine the combined mass of its components:
Copper -63has 29 protons and 34 neutrons. The mass of a proton is 1.00728 amu and a neutron is 1.00867 amu.The ‘separated’ mass is:
29 protons(1.00728 amu/proton) + 34 neutrons(1.00867 amu/neutron) =
Dm = 63.50590 amu - 62.91367 amu = 0.59223 amu
We’ll practice calculating mass defect and binding energy, but first… a quick discussion about units:
What is a Joule?
Well, if E = mc2 , then the units of E will be kg (m/s)2.
You will discover in physics that units are often named after somebody and/or replaced by a reference value (i.e. "amu" refers to the mass of a carbon atom). So, kg (m/s)2. is called a Joule.
Not a hammie.
Example 3 The Binding Energy of the Helium Nucleus Revisited
The atomic mass of helium is 4.0026u and the atomic mass of hydrogen
is 1.0078u. Using atomic mass units, instead of kilograms, obtain the
binding energy of the helium nucleus.
Calculate this mass!
Use the information given in the problem and at the top of the screen.
Now, calculate the mass defect.
Find the binding energy two ways:
(1) Convert the △m into kg, then use E = mc2. Convert into eV.
(2) Notice method (1) isn’t much fun. So, convert △m directly into MeV.
Compare your answers.
Too much work for me to type up! Your answer should be about 28.3 MeV
1 u = 931.5 Mev so 0.0304(931.5) = 28.3 MeV
Graph of Binding Energy per nucleon
Nuclear transmutation: the conversion of one chemical element or isotope into another through a nuclear reaction
When an unstable or radioactive nucleus disintegrates spontaneously, certain types of particles and/or high-energy photons are released. These particles and photons are collectively called ‘rays’. Three kinds of rays are produced by naturally occurring radioactivity. They are named according to the first three letters of the Greek alphabet, alpha, beta, and gamma.
These processes must obey all the laws of physics that we have studied so far, or are yet to study. Nuclei undergoing radioactive decay must obey all the laws of conservation, including one new to us – the nucleon number. Conservation Laws tell us that these things must be ‘preserved’ – we don’t magically lose mass/energy, or charge, or momentum. And we don’t lose nucleons in radioactive decay.
The FIVE energy Conservation Laws:
So, an interesting experiment was done. Some radioactive material was surrounded by lead, except for one small hole. It is known that thick lead plates can stop radioactive particles, and this would allow the particles to escape from the hole but only in one direction.
Next, a photographic plate was placed a short distance away which would be exposed by high-energy particles. Finally, all this was placed in a chamber, and the air was extracted, creating a vacuum.
And finally, the chamber was placed into a magnetic field.
So, what did they discover?
Some particles went ‘up’, some particles went ‘down’ and some went straight on through.
We will learn in our EM unit that a positive charge will be deflected upwards in this orientation of a magnetic field. A negative charge downward. And an uncharged particle is not affected by the magnetic field.
So, it was discovered that THREE types of particles are created during radioactive decay.
Further experiments discovered that those positively charged particles, called alpha-particles (from alpha-decay) are easily blocked by think lead plates (.01 mm). This indicates they have less energy than the other particles. Their symbol isα. This type of radiation is a Helium nucleus (without the electron).
The negatively charged particles, beta-particles (beta-decay) are blocked by .1 mm lead. Their symbol isβ. This type of radiation is an electron emission.
And the uncharged gamma particles could pass through 100 mm of lead. They have a lot of energy, so it takes a lot of energy to stop those buggers. Their symbol isγ. This type of radiation is a photon emission.
During beta decay, energy is released. However, it is found that
most beta particles do not have enough kinetic energy to account for
all of the energy released.
The additional energy is carried away by a neutrino.
The sequential decay of one nucleus after another is
called a radioactive decay series.
Extra Topics In
The half-life of a radioactive
decay is the time in which ½
of the radioactive nuclei
Conceptual Example 12 Dating a Bottle of Wine
A bottle of red wine is thought to have been sealed about 5 years
ago. The wine contains a number of different atoms, including carbon,
oxygen, and hydrogen. The radioactive isotope of carbon is the
familiar C-14 with ½ life 5730 yr. The radioactive isotope of oxygen
is O-15 with a ½ life of 122.2 s. The radioactive isotope of hydrogen
is called tritium and has a ½ life of 12.33 yr. The activity of each
of these isotopes is known at the time the bottle was sealed. However,
only one of the isotopes is useful for determining the age of the
wine. Which is it?
A Geiger counter