Radioactivity

Types of particles:Alpha particles

• Two protons + two neutrons

• Same as helium-4 nucleus

• + 2 charge; deflected by a magnetic field, and attracted to negative charges

Alpha particles

• Largest particle of radioactivity

• Short range• Stopped by sheet of

paper• Most damaging due

to large mass

Alpha tracks in a cloud chamber

Nuclear equations

• Mass must be conserved• Mass numbers and atomic numbers must have same

sum on each side of equation• Result of alpha emission: mass number decreases by 4,

atomic number decreases by 2• Note symbol for alpha particle – sometimes

writtenor just

Beta Particles

• Consist of free electrons

• Low mass, -1 charge• Medium range,

medium penetrating power

• Stopped by thick wood, thin sheet of lead

• Symbol is the Greek

letter beta or 0-1e

• Produced by a neutron, which turns into a proton

Nuclear equations

• In beta decay a neutron turns into a proton and ejects an electron

• Mass number does not change, and atomic number increases by 1

• Example of transmutation

Gamma Radiation

• Consists of high-energy photons

• No rest mass, no charge

• Not deflected by magnetic field

• Long range, very penetrating

• Accompanies many other types of decay

• Symbol is Greek letter

gamma• Only product of IT –

internal transition• Produces no change

of mass or atomic numbers

Other types of decay

Positron Emission• Positrons are the

electron’s antiparticle• Same characteristics

as electron, except for positive charge

• Symbol: + or 01e

Positron Emission Tomography(PET scan)

Positron emission

• In positron emission a proton ejects a positron and becomes a neutron

• Mass number does not change• Atomic number decreases by one

Electron Capture

• If there are too many protons in a nucleus, it may capture an electron

• A proton becomes a neutron

Symbol for an electron

Electron capture

• Mass number stays the same• Atomic number decreases by one• Same result as positron emission

Nuclear Stability

• Nuclear particles (protons and neutrons) are called nucleons

• Nucleons are held together by nuclear strong force (short range, very strong)

• Neutrons are “glue” – necessary to hold the nucleus together

• Without neutrons the nucleus would fly apart due to electrostatic repulsion

Nuclear Band of Stability

Stability and Decay

• Above the stability band: Too many neutrons

• Beta decay reduces the neutron/proton ratio

• Very large nuclei (Z>83) undergo alpha decay, which reduces the size of the nucleus

Stability and decay

• Below the band of stability: too many protons

• Positron emission or electron capture

• Protons are reduced, neutrons increased1

1p 10n + 0

1

11p + 0

-1e 10n

Nuclear Magic Numbers

• Nuclei with certain numbers of protons or neutrons are especially stable

• “Magic numbers” are 2, 8, 20, 28, 50, 82, and 126

• When both neutrons and protons are magic numbers, the nucleus is specially stable: 208

82Pb

Nuclear Magic Numbers

• Most stable nuclei have the same “magic number” of protons and neutrons: 4

2He, 16

8O, and 4020Ca

• “Even-odd” rule: Nuclei with even numbers of protons and neutrons are more stable than odds:

• Stable isotopes: 264

• Both even: 157 Both odd: 5

Decay series

Induced Transmutation

• Transmutation can be induced by allowing high-energy particles to strike atomic nuclei

42He + 14

7N 178O + 1

1p238

92U + 10n 239

92U 23993Np + 0

-1e239

93Np 23994Pu + 0

-1e

10n + 14

7N 146C + 1

1H

Radioactive Decay

• Radioactive isotopes decay at predictable rates

• Half Life: the time it takes for 1/2 of a sample to decay

• Half of the remaining sample decays every half life period

Radioactive decayRadioactive decay

Half Life Graph

Half Life

• Follows exponential decay

• Moment of decay of any one particle is unpredictable

• Example: Radon-222 decays with a half life of 3.8 days. Approximately how long will it take for 9.5 grams of a 10 gram sample to decay?

Half Life Problems

• Solution: Divide sample mass in half until 0.5 grams or less is reached.

10/2 = 5 (one half life)

5/2 = 2.5 (two half lives)

2.5/2 = 1.25 (three half lives)

1.25/2 = 0.625 (four half lives)

0.625/2 = 0.3125 (five half lives)

Half life Problems

• Four half lives = 4 HL x 3.8 days/HL = 15.2 days

• Five half lives = 5 HL x 3.8 days/HL = 19 days

• Therefore, 9.5 grams of a 10 gram sample will decay in somewhere between 15.2 and 19 days.

Half Life Problems

• Example #2: Sally has a 15.0 g sample of phosphorus-32 (half life 14.28 days). About how much will be left two months later (60 days)?

• Find time in half-lives: 60 days/14.28 days/HL = 4.20 half lives.

• Multiply the sample mass by (1/2)y, where y = number of half-lives (use xy key on calculator)

Half Life Problems

• 15.0g(1/2)4.20 = 15.0g(0.0544) = 0.816 g remaining

• Half life equation: Nt = N0(1/2)t/t1/2 or

Nt = N0e-t where is the decay constant

t = (t1/2/0.693)ln(N0/Nt)

Nuclear Reactions and Energy• Mass is not strictly conserved in nuclear

reactions• Some mass is lost as energy

Nuclear Reactions and Energy

• Mass to energy conversion is governed by E = mc2, where c = the speed of light in a vacuum (3.0x108m/s)

• Nuclear binding energy is the energy lost when the nucleus is formed.

• Mass equivalent of the nuclear binding energy is the mass defect.

• Protons and neutrons in the nucleus have less mass than separate nucleons

http://upload.wikimedia.org/wikipedia/commons/5/53/Binding_energy_curve_-_common_isotopes.svg

Calculating Binding Energy

• Example:

• Mass of 1 proton = 1.00735 amu

• Mass of 1 neutron = 1.00875 amu

• Mass of 1 electron = 0.0005485 amu

• If 1 amu = 1.66 x 10-24g, calculate the binding energy of an atom of helium-4 (mass 4.00260325415 amu)

Binding energy of helium-4

• Mass of constituents Protons: 1.00735 amu/p(2p) = 2.01470 amuNeutrons: 1.00875 amu/n(2n) = 2.01750 amuElectrons: 0.0005485 amu/e(2e) = 0.001097 amuTotal: 4.03330 amu4.03330 amu(1.66x10-24g/amu) = 6.70x10-24gHelium atom: 4.0026amu(1.66x10-24g/amu) = 6.64x10-24g)

Binding energy of helium-4

• Mass deficit = 6.70x10-24g - 6.64x10-24g = 0.06x10-24g = 6x10-26g = 6x10-29kg

• Binding energy: E = mc2

• E = 6x10-29kg(3.00x108m/s)2 = 5x10-12J

• Energy per gram: one gram of helium-4 would have 1g/(6.64x10-24) = 1.51x1023 atoms

• 1.51x1023 a/g(5 x 10-12J/a) = 8 x 1011J/g

Binding energy of helium-4

• 8 x 1011J/g(1 kW-hr/3600 J) = 2 x 108 kW-hr• Average household uses 10,656 kW-hr/yr• 2 x 108 kW-hr/10,656 kW-hr/(house-yr) = 20,000• Binding energy in one gram of helium-4 could

power 20,000 average households for one year• Alternatively, it could power one house for

20,000 years, or Al Gore’s mansion for 904 years.

Nuclear Fission

• Some larger nuclei will split into two parts when struck by a neutron

• The two smaller nuclei are more stable, so energy is released

• The two smaller nuclei will have a higher binding energy per nucleon

• Neutrons are also released, producing a chain reaction

Nuclear Fission

Nuclear chain reactions

• Occur if the product of the reaction is necessary to start new reactions

10n + 235

92U --> 23692U --> 92

36Kr + 14156Ba + 31

0n

• Critical mass - minimum mass necessary to sustain a chain reaction

• Large enough critical mass will explode

Nuclear Power Plants

• Nuclear fuel is usually a supercritical mass of U-235 enriched uranium

• Reaction is promoted by a moderator - a material that slows neutrons down so they will cause fission - usually carbon or D2O

Nuclear reactor at Chernobyl

Nuclear Power Plants

• Reaction is controlled by control rods (cadmium or boron), which absorb neutrons

• Reaction generates heat, which makes steam to run a turbine

CROCUS, a small research nuclear reactor

Geiger Counter

• Counts individual particles of radioactivity

• Ionizing radiation enters the tube through a mica window

• Ionization of gas in tube allows current to flow for an instant between high voltage cathode and anode