Conservation of Mass and Energy
 Nuclear chemistry forces us to modify the Law of Conservation of Mass to include an energy term as well. The energy term is derived from Albert Einstein's famous E=mc2 equation. Actually this equation was rewritten for the layman, in its true form it is E = moc2, where E is the change in energy that takes place, mo is the change in rest mass, and c is the speed of light. Because the speed of light is very large and it's square even larger, even a very small change in mass would translate into an enormous change in energy. For example lets take a look at an ordinary chemical reaction.

The combustion of the gas methane.

CH4(g) + 2 O2(g) ---> CO2(g) + 2 H2O(g)      Ho = -890 kJ/mol
since E = moc2 then upon rearrangement we get mo = E
c2
Fact: 1 J = 1 kg m2 This a fact that should be memorized.
s2
therefore mo = ___890 kJ     X 1000 J  1 kg m2
(3.0 x 108 m)2       1 kJ              s2

= 9.89 x 10-12 kg

= 9.89 x 100 ng

The 890 kJ of energy released by the combustion of one mole of methane thus originates from the conversion of 9.89 ng of mass into energy. Such a small change, about 10 ng out of 80 g cannot be detected by balances. It amounts to the loss of 1.0 x 10-7% of the mass. So we ignore Einstein's equation when doing regular chemical stoichiometric calculations. However this equation is very useful in nuclear chemistry.

Nuclear Binding Energy
The sum of the rest masses of the nucleons of an atom does not equal the measured mass of any nucleus. The actual mass of an atomic nucleus is always a trifle smaller then the sum of the rest masses of all it's nucleons (p+ + no). This mass difference is changed into energy as the nucleus formed, and was emitted as high energy electromagnetic radiation. It would cost this much energy to break the nucleus apart into its nucleons again, so the energy is called the 'binding energy of the nucleus'.
Lets take a look at the manufacture of a Helium nucleus.
Binding energy of 42He - actual rest mass is 4.001506 amu.
The rest masses of the nucleons are:
p+ = 1.007277 amu no = 1.008665 amu You should include these numbers in your data book.

For 42He then 2 p+ = 2 x 1.007277 amu = 2.014554 amu
2 no = 2 x 1.008665 amu = 2.017330 amu
4.031884 amu

The difference in mass = calculated mass - actual mass
= 4.031884 amu - 4.001506 amu
= 0.030378 amu
1 kg = 1000 g          1 amu = 1.6606 x 10-24 g {Include these facts as well}

so

E = moc2

= (0.030378 amu X 1.6606 x 1024 g  1 kg    )(3.0 x 108 m)2
amu           1000 g                     s
= 4.54 x 10-12 kg m2
s2
= 4.54 x 10-12 J This is the energy release for 1 atom of 42He
A mole of He would be 6.02 x 1023 nuclei more, therefore,
6.02 x 1023 nuclei/mole * 4.54 x 10-12 J/nuclei
= 2.73 x 1012 J/mole (enough energy to power a 100 watt light bulb for 900 years)
How do I know this?
P=E/t from grade 11 chemistry class.

therefore t = E/P

= 2.73 x 1012 J
100 W

= 2.73 x 1012 J
100 J/s

= 2.73 x 1010 s (X 1 min/60 s)

= 4.55 x 108 min (X 1 hr/60 min)

= 7.583 x 106 h (X 1 day/24 h)

= 315972.2 days (X 1 y/365.25 days)

= 865.09 years

Go to the Nuclear Conservation of Energy Worksheet

The Curve Of Binding Energy
The zone of highest stability lies between Fe-56 and Br-66.

The curve passes through a maximum at iron-56. The nuclei become less stable as the mass numbers become higher therefore we can expect atoms with higher atomic numbers to fission and break into smaller more stable isotopes, On the other hand, it would be the fusion of the lower atomic number nuclei which would result in more stable isotopes. For this reason it is H and He with which fusion attempts are being made.

Transmutation
When a high speed particle is captured by a nucleus, the nucleus can be permanently changed to that of another element. The changing of one isotope to another is called transmutation, and radioactive decay is just one way this can happen. Another way is by bombarding the atoms of an isotope with high-energy particles. Usually these are alpha particles from natural alpha emitters, neutrons from atomic reactors and p+ made by the removal of electrons from H atoms. Alphas and p+ are suitable for acceleration to ultrahigh energies in special accelerators. With sufficient energy, bombarding particles can shoot through the e- orbitals and bury themselves in nuclei. Beta particles are strongly repelled by the orbital e- and are therefore seldom used. When a nucleus captures a bombarding particle it becomes a compound nucleus. At the moment of impact, it has all the energy of the bombarding particle and is therefore unstable. The nucleus must get rid of this excess energy. It can do this by ejecting a high energy particle such as a neutron, a p+, or an e- along with radiation.

The first transmutation was performed by E. Rutherford

alpha  + 147N ---> 169F + 11p+ ------> 158

The first artificial accelerator reaction

11p+ + 73Li ---> 84Be ---> 2 42He

Transmutation can be performed on any number of isotopes. Once the new isotope is formed it can then undergo many types of emission to create a variety of new isotopes. Below is an example. The different reactions can be used to make Al-27 but once the Al-27 is made it can under go decay into 5 different isotopes.

---> 2311Na + (stable)
|
42He + 2311Na ----- ---> 2512Mg + p+ + no (stable)
|                              |
11p + 2612Mg --------> 2713Al -------> 2612Mg + 11p (stable)
|                          |
21D + 2512Mg ----- ---> 2713Al + (stabilized)
|
---> 2612Al + 10n (unstable)
t½ = 7.4 x 105

Go to the Nuclear Transmutation Worksheet

The ability of radiation to generate ions in matter makes their detection and measurement possible. All of the radiations studied so far are ionizing radiations.  When ions are produced in a gas, even momentarily they become a conductor.

Geiger Counters

Cloud Chambers
A beaker or dish of supersaturated alcohol vapour. When a particle streaks through it, it ionizes a trail through the vapour. The alcohol vapours condense out around the trail and they become visible. You don't see the particle, only the trail they left behind.

Scintillation Counters
A device that permits an investigator to see when a collision occurs between a particle and a special surface on the counter. This surface is coated with a substance that gives off a tiny light flash when it is hit by a particle of radiation. For example, if the coating contains zinc sulphide phosphor, then an alpha particle will cause visible scintillations. A TV screen and a fluorescent tube are both scintillation screens with phosphors that react to particles.

Dosimeter
A dosimeter is used to measure the total quantity of radiation received by a surface during a specified period of time. Some dosimeters use photographic plates that are kept completely shielded (from visible light) but that are sensitive to radiations. The amount of darkening is proportional to the amount of received radiation. The dosimeter is made up of a plate of photographic emulsion and is covered by three layers. One layer is lead and will stop alpha and beta radiation so only gamma will get through. The plastic cover will let gamma and beta through but not alpha. The last cover is paper, thick enough to stop light from getting to the emulsion but thin enough to let alpha particle through. The emulsion is developed just like a regular black and white picture. The degree of darkening in each area gives a breakdown and dosage for each of the three types of radiations.

Those who routinely work with radioactive materials should use radiation shielding and they should stay as far as practical from the source of the radiation. Cardboard, aluminum and plastic are relatively poor shields, but lead and concrete (if thick enough) are relatively good and inexpensive materials. Keeping one's distance from a radioactive source is effective in providing radiation protection because the intensity of the radiation diminishes with the square of the distance from the source. Thus if a worker doubles the distance, the exposure is reduced by ¼. The relationship between distance and intensity is given by the inverse square law

d2

where d is the distance from the source. If the intensity, I1 is known at distance, d1, then the intensity, I2, at distance, d2, can be calculated as:

I1d22
I2     d12

This law applies only to a small source that radiates equally in all directions and with no intervening shields.

eg. At 1.5 m from a radioactive source the radiation intensity is 40 units. If the operator moves to a distance of 4.5 m from the source, what will be the radiation intensity?

40 units = (4.5 m)2
I2         (1.5 m)2

I2 = 40 units X (1.5 m)2
(4.5 m)2

=  4.4 units

Becquerel and Curie
When a radioactive sample is purchased what is of particular interest is its activity. Activity refers to the number of nuclear disintegrations per second that occur in a sample. The nuclear SI unit is the Becquerel (Bq) which is 1 disintegration/second. The older unit, the Curie(Ci) is defined as 1 Ci = 3.7 x 1010 disintegrations per second. If a hospital has a source rated at 1.5 Ci then the source delivers 1.5 x 3.7 x 1010 = 5.6 x 1010 Bq.

The 'rad' is used to describe the quantity or dose of radiation absorbed by some material. The most common unit is the rad(rd) which stands for radiation absorbed dose) and it is defined as 10-5 J/g of material. The SI unit of absorbed dose if the Gray(Gy).

1 Gy = 1 J/kg of material

therefore 1 rd = 10-5 J/g

1 Gy = 1 J/kg

therefore 1 Gy = 100 rd

REM
The rad does not account for the kind of damage done, only for how much radiation goes in. Neutrons are more dangerous then radiation of the same energy and intensity. To take into account this fact the REM was derived. To find the dose in REMS the dosage in rads is multiplied by a conversion factor that reflects the effectiveness of the kind of radiation causing the damage.

Conversion factors  ??? = 20
no = 2 - 10 depending upon their speed
alpha , beta , X-rays = 1

Radioactivity can ionize molecules. ie; as the particulate radiation hits a molecule it can knock electrons out of orbit. The ionized molecule will then chemically react with adjoining molecules to form new compounds. These fragments and new compounds can alter cellular processes and functions. Even gamma rays can excite electrons out of orbit, leaving behind an ion. If radiation passes through a normal body cell the damage is said to be somatic. If the radiation passes through a sex cell the chromosomes may be damaged. Given time, without division the cell can repair this damage. But if a cell is undergoing meiosis or mitosis the damage can be passed on to a new cell without any repairs being implemented. These errors in the DNA code result in mutations of the DNA

Dosage in REMS Biological Effect

25    notable change in blood cell components

100  radiation sickness - nausea, vomiting, decrease in white blood cell count, diarrhea, dehydration, prostration, haemorrhaging and loss of hair

200  the same as above but more pronounced in a shorter period of time

400  LD50 limit - ½ of any population exposed to this dosage will be dead in 60 days

600  all exposed to this level will be dead in one week

Chernobyl - Anyone near the Chernobyl plant received 400 rems also immediately. The day after 1 rem/hr was found in the nearest city. Normal background radiation is 1,000 times lower than this.

In Canada the Labour Relations Act specifies that radiation workers or anyone or works with radiation can be safely exposed to 0.3 rem/hr only. A typical X-ray that you get taken gives you only 7 mrem.

No one can escape low level exposure to radiation. Radioactive sources are everywhere and together they make up what is called the natural background radiation and this gives an average of about 160 mrem of exposure/year/person. This radiation includes cosmic rays from above and radiations from radionuclides in the earth. C-14 is present in all the food we eat. The human body (adult) has approximately 5 x 105 disintegrations/minute.

Tracer Analysis
Tracer chemicals are used to locate areas of concentration. If these chemicals are radioactive then they can be found easily with a radiation scanner. The most favoured is pertechnitate ion TcO4- which brain tumours seem to be able to concentrate readily. The pertechnitate ion, which is made from technicium-99m(metastable) drops from Tc-99m to Tc-99 as it gives off a burst of gamma radiation. The whole body scanner will pick up this burst and display it on a computer terminal.

Iodine-131, a beta emitter(T½ = 8.07 d) is used to test thyroid function.
Plants dipped in solutions consisting of HCO3- ions made from C-14 (t½ = 5730 y, ). When the plant uses this ion we can determine not only what compounds are made but which C's in each individual molecules consists of C-14 instead of C-12.

Neutron Activation Analysis
A technique for analyzing the concentration of some element in a substance. It is based on the fact that a number of stable nuclei can be changed into a gamma radiation emitter by capturing neutrons.

MAX + 10n ---> M+1AX ---> M+1AX +

But each kind of neutron enriched nuclei emits gamma radiation at its own unique frequencies. By measuring the frequencies emitted, the element can be identified. By measuring the intensity of the gamma radiation, the concentration of the elements can be determined. This technique is so sensitive that concentrations as low as 10-9% can be determined.