Science help!!?

Question

Describe the concept of using radioactive elements to establish an age for a fossil. Be sure to include how the parent and daughter elements are used in the determination of age.

Answer 1

All radioactive isotopes, which are elements that have the same number of protons but different numbers of neutrons, lose mass (as a percent of total mass) at a constant rate. The "half life" is the number of years any sized mass sample of an isotope takes to lose 1/2 of its mass. The decay process results in the emission of alpha particles (actually a 4 2Helium nucleus) or the emission/capture of an electron (beta-negative), depending on the nature of the isotope

The simplest way to depict the decay is to have the original isotope in question depicted on the left-hand side, and then show the particles that are emitted on the right side. Make sure the superscript (the atomic mass) and the subscript(the atomic number) add up to the values on the original isotope. For example, a Beta particle, an electron, has a 0 -1 value (0 is the mass, -1 is the charge, which is the opposite of the atomic number that is depicted by + protons).

Scientists take samples of unknown age and measure the radioactivity in a given sample. The idea is that if a sample is younger, it will give off more particles per unit of time because even though the rate of decay (as % of a sample mass) is constant, there is more mass to work with when the sample has had less time to decay. For example, a 4 g sample of carbon-containing matter that is about 5700 years old will give off 1/2 as many alpha particles than a fresh 4g sample, because the half life of C-14 is about 5700 years. (Half of more is more than half of less). Scientists use this knowledge to give them estimates of the age of a sample. For C-14, scientists assume that once plant or animal matter dies, the original C-14 amount begins to decay at a constant rate (it is not replenished by solar radiation).

The formula to roughly calculate the mass of a sample left after t years is:

Mass Remaining=Initial mass*e^rt

where e = constant 2.718
r=rate of decay
t=time

A formula for half life is:

.693/t=r
or
.693/r=t