NUCLEAR DECAY

How Many Neutrons? The number of neutrons in a nucleus can vary Range limited by the degree of instability created by having too many neutrons too few neutrons Stable nuclei do not decay spontaneously Unstable nuclei have a certain probability to decay

Nuclear Stability Facts 270 Stable nuclides 1700 radionuclides Every element has at least one one radioisotope For light elements (Z20), Z:N ratio is ~1 Z:N ratio increases toward 1.5 for heavy elements For Z>83, all isotopes are radioactive

Nuclear Stability Facts The greater the number of protons, the more neutrons are needed “Magic numbers” of protons or neutrons which are unusually stable 2, 8, 20, 28, 50, 82, 126 Sn (Z=50) has 10 isotopes; In (Z=49)& Sb (Z=51) have only 2 Pb-208 has a double magic number (126n, 82p) & is very stable

Band of Nuclear Stability Stable isotopes form a band of stability from H to U Z:N ratios to either side of this band are too unstable & are not known

Nuclear Band of Stability

Radioactivity The spontaneous decomposition of an unstable nucleus into a more stable nucleus by releasing fragments or energy. Sometimes it releases both.

Electromagnetic Radiation Electromagnetic radiation is a form of energy that can pass through empty space The shorter the wavelength, the more energy it possesses gamma rays are very energetic radio waves are not ver energetic

TYPES OF RADIOACTIVE DECAY

Alpha Emission ZAX Z-2A-4Y + 24 92235U 90231Th + 24 Identity of the atom changes Quick way for a large atom to lose a lot of nucleons (increases N:P ratio)

Beta Emission Ejection of a high speed electron from the nucleus ZAX Z+1AY + -10 1940K 2040Ca + -10 Decrease N:P ratio; identity of atom changes

Gamma Emission Emission of high energy electromagnetic radiation Usually occurs after emission of a decay particle forms a metastable nucleus Does not change the isotope or element

Radiation Energetics Alpha Particles relatively heavy and doubly charged lose energy quickly in matter Beta Particles much smaller and singly charged interact more slowly with matter Gamma Rays & X-rays high energy more lengthy interaction with matter

PENETRATING DISTANCES alpha beta gamma

PENETRATING DISTANCES paper alpha beta gamma

PENETRATING DISTANCES paper alpha beta gamma aluminum

PENETRATING DISTANCES paper alpha beta lead gamma aluminum

HAZARDS POSED BY DIFFERENT TYPES OF RADIATION Alpha Emissions easily shielded considered hazardous if alpha emitting material is ingested or inhaled Beta Emissions shielded by thin layers of material considered hazardous when beta emitter is ingested or inhaled Gamma Emissions need dense material for shielding considered hazardous when external to the body

Radioactive Decay Rates Relative stability of nuclei can be expressed in terms of the time required for half of the sample to decay Examples: time for 1 g to decay to .5 g Co-60 5 yr Cu-64 13 h U-238 4.51 x 109 yr U-235 7.1 x 108 yr

HALF-LIFE The level of radioactivity of an isotope is inversely proportional to its half-life. The shorter the half-life, more unstable the nucleus The half-life of a radionuclide is constant Rate of disintegration is independent of temperature or the number of radioactive nuclei present

The grid below represents a quantity of C14. Each time you click, one half-life goes by. C14 – blue N14 - red Half lives % C14 %N14 Ratio of C14 to N14 100% 0% no ratio As we begin notice that no time has gone by and that 100% of the material is C14 Age = 0 half lives (5700 x 0 = 0 yrs)

The grid below represents a quantity of C14. Each time you click, one half-life goes by. C14 – blue N14 - red Half lives % C14 %N14 Ratio of C14 to N14 100% 0% no ratio 1 50% 1:1 After 1 half-life (5700 years), 50% of the C14 has decayed into N14. The ratio of C14 to N14 is 1:1. There are equal amounts of the 2 elements. Age = 1 half lives (5700 x 1 = 5700 yrs)

The grid below represents a quantity of C14. Each time you click, one half-life goes by. C14 – blue N14 - red Half lives % C14 %N14 Ratio of C14 to N14 100% 0% no ratio 1 50% 1:1 2 25% 75% 1:3 Now 2 half-lives have gone by for a total of 11,400 years. Half of the C14 that was present at the end of half-life #1 has now decayed to N14. Notice the C:N ratio. It will be useful later. Age = 2 half lives (5700 x 2 = 11,400 yrs)

The grid below represents a quantity of C14. Each time you click, one half-life goes by. C14 – blue N14 - red Half lives % C14 %N14 Ratio of C14 to N14 100% 0% no ratio 1 50% 1:1 2 25% 75% 1:3 3 12.5% 87.5% 1:7 After 3 half-lives (17,100 years) only 12.5% of the original C14 remains. For each half-life period half of the material present decays. And again, notice the ratio, 1:7 Age = 3 half lives (5700 x 3 = 17,100 yrs)

How can we find the age of a sample without knowing how C14 – blue N14 - red How can we find the age of a sample without knowing how much C14 was in it to begin with? 1) Send the sample to a lab which will determine the C14 : N14 ratio. 2) Use the ratio to determine how many half lives have gone by since the sample formed. Remember, 1:1 ratio = 1 half life 1:3 ratio = 2 half lives 1:7 ratio = 3 half lives In the example above, the ratio is 1:3. 3) Look up the half life and multiply that that value times the number of half lives determined by the ratio. If the sample has a ratio of 1:3 that means it is 2 half lives old. If the half life of C14 is 5,700 years then the sample is 2 x 5,700 or 11,400 years old.

C14 has a short half life and can only be used on organic material. To date an ancient rock, use the uranium–lead method (U238 : Pb206). Here is our sample. Remember we have no idea how much U238 was in the rock originally but all we need is the U:Pb ratio in the rock today. This can be obtained by standard laboratory techniques. As you can see the U:Pb ratio is 1:1. From what we saw earlier a 1:1 ratio means that 1 half life has passed. Rock Sample Now all we have to do is see what the half-life for U238 is. We can find that information in half-life reference tables. 1 half-life = 4.5 x 109 years (4.5 billion), so the rock is 4.5 billion years old.

Element X (Blue) decays into Element Y (red) The half life of element X is 2000 years. How old is our sample? See if this helps: 1 HL = 1:1 ratio 2 HL = 1:3 3 HL = 1:7 4 HL = 1:15 If you said that the sample was 8,000 years old, you understand radioactive dating.

Element X (blue) Element Y (red) How old is our sample? We know that the sample was originally 100% element X. There are three questions: First: What is the X:Y ratio now? Second: How many half-lives had to go by to reach this ratio? Third: How many years does this number of half-lives represent? 1) There is 1 blue square and 15 red squares. Count them. This is a 1:15 ratio. 2) As seen in the list on the previous slide, 4 half-lives must go by in order to reach a 1:15 ratio. 3) Since the half life of element X is 2,000 years, four half-lives would be 4 x 2,000 or 8,000 years. This is the age of the sample.

The half-life of this element is 1 million years. Question may involve graphs like this one. The most common questions are: "What is the half-life of this element?" Just remember that at the end of one half-life, 50% of the element will remain. Find 50% on the vertical axis, Follow the blue line over to the red curve and drop straight down to find the answer: The half-life of this element is 1 million years.

After 2 million years 25% of the original material will remain. Another common question is: "What percent of the material originally present will remain after 2 million years?" Find 2 million years on the bottom, horizontal axis. Then follow the green line up to the red curve. Go to the left and find the answer. After 2 million years 25% of the original material will remain.

Trying To Reach Nuclear Stability Some nuclides (particularly those Z>83) cannot attain a stable, nonradioactive nucleus by a single emission. The product of such an emission is itself radioactive and will undergo a further decay process. Heavy nuclei may undergo a whole decay series of nuclear disintegrations before reaching a nonradioactive product.

The Four Known Decay Series

Decay Series A series of elements produced from the successive emission of alpha & beta particles

RADON GAS

Radon-222 Originates from U-238 which occurs naturally in most types of granite Radon-222 has a half-life of 3.825 days It decays via alpha emissions This isotope is a particular problem because it is a gas which can leave the surrounding rock and enter buildings with the atmospheric air