Half-Life and Nuclear Stability

How many isotopes are stable? So far, 118 different elements have been isolated. Only 92 of these are naturally occurring; all elements with Z>92 are artificial. For those 118 elements, approximately 1500 nuclei are known. But only 279 are stable – their nuclei do not change over time. The stability of the nucleus is largely dependent on the ratio of protons and neutrons.

The Zone of Stability

Zone of Stability For Z<20, the optimal ratio is 1:1. For Z>20, the ratio increases to 1:1.5. (actually more like 3:5)

Why Alpha, Why Beta? Elements that have too many neutrons (to the left of the blue area) undergo beta emission (neutron decay) Elements that have too few neutrons (to the right of the blue line) undergo positron emission or electron capture. Just above the top of the blue area, where the heaviest elements are, atoms commonly undergo alpha emission.

What’s the Secret to Stability? Number of Protons Number of Neutrons Number of Stable Isotopes Even 168 EvenOdd57 OddEven50 Odd 4

Half-Life The half-life is the time required for a substance to decay to 1/2 of its initial value. Note that this phrase is also used to describe the persistence of chemicals in the body and/or the environment, and is not limited to radioactive substances. Half lives can range from nanoseconds for some of the artificial radioisotopes, to billions of years. 238 U, with a half-life of 4.5 x 10 9 years.

Uranium-238 Decay Series This process is responsible for much of the earth’s internal energy. Half-lives range from billions of years to fraction of seconds. Some isotopes have multiple decay modes.

Multiple Half Lives Taking a short-lived radioisotope as an example: 131 I has a half-life of 8 days. If we begin with 32 mg of iodine-131, 32 mg So after 40 days, only 1 mg of iodine-131 remains. What has happened to the rest? It has been transformed into other substances. Sometimes a complex series of intermediates are involved before a stable isotope is reached.

I-131 Decay Curve

Lab 4: Modeling Radioactive Decay (Half-Life) Objective To use a model to study radioactive decay in order to learn how it can be used to determine the age of an object. Materials 100 pennies

Procedure Pour bag of pennies on the table. Place them face up, and count them all. If you have less than 100, get some extras from the teacher. Let the “heads” side represent the original radioactive state before decay. The “tails” side represents the decayed, non-radioactive stable state. Put the pennies back in the bag. Then pour them back onto the table. Remove and count all of the decayed “tails” pennies. Record in the data table on the following page. Count the remaining “heads” pennies. Place them back in the bag and repeat steps 3 and 4. Repeat the procedure until you are left with a maximum of one undecayed “atom.” Calculate the percentage that decayed during each trial using the following formula: % decaying = Number of decayed objects removed x 100 Number of objects before shaking Use your data table values to draw a graph of the number remaining (number of objects before shaking) versus trial number.

Data Table Trial #Number of objects before decayingNumber of objects “decayed”% decaying

Four Types of Half-Life Problems How much is left? HL, time elapsed, and initial mass are given. 56 Mn undergoes beta emission with a half life of 2.6 hours. What is the mass of a 1 mg sample of the isotope after 10.4 hours?

At the time of superman’s birth, a pure sample of 85 Kr was prepared to hasten his demise. At the time of superman’s death 86 years later, what fraction of the original sample remained?

How long did it take? HL, amount remaining or decayed is given. With a half-life of 28.8 years, how long will it take for 1 g of strontium-90 to decay to g?

How old is it? A sample of fossilized wood originally contained 24 g of carbon-14 when it was alive. It now contains 1.5 g. How old is the sample?

What is the half-life? Time elapsed is given, initial and final mass is given. A 64 g sample of Germanium-66 is left undisturbed for 12.5 hours. At the end of that period, only 2.0 g remains. What is the half-life of this material?

What is the half-life? What is the half-life of Polonium-214 if, after 820 seconds, a 1.0 g sample decays to g?

How much did you start with? HL is given, final mass is given. You have to work backwards here! Cobalt-60 has a half-life of 5.3 years. If a pellet that has been in storage for 26.5 years contains 14.5 g of Co-60, how much was present when the pellet was put into storage?

How much did you start with? A sample of air from a basement is collected to test for the presence of radon-222. However, delays prevent the sample from being tested until 7.6 days have passed. Measurements indicate the presence of 6.5 μg of radon-222. How much was present in the original sample?