- The inverse square law of radiation states that the intensity of radiation becomes weaker as it gets further from the source (NDT Resource Center, n.d.). To determine the Geiger counter reading that we would get for a radioactive material when we are three feet away from the source, assuming an initial reading of 6300 R at a distance of one foot from the source, we must use the formula:
(I1/I2) = (D22/D12)
In this case, D1 is 1 foot, D2 is three feet, I1 is 6300 R. Plugging these numbers into the above equation, we get (6300/I2) = (32/12), which is equal to (6300/I2) = (9). When solving for the missing variable, we get I2 = 6300/9, which is 700 R.
- To determine how many atoms will remain in Dr. Brown’s radioisotope source after 352 years, we must use the radioactive decay formula, N(t) = N0e-lambda*t, in which N(t) represents the number of atoms remaining after the decay, N0 represents the initial population of the atoms, lambda is the decay constant, and t represents time (Think Quest, n.d.). In this example, N0 is 1.2 x 106, t is 352 years, and the lambda (the decay constant of Plutonium-238) is 2.51 x 10-10 First we must convert 352 years into seconds so the decay constant and the time have the same unit (352 years x 365 days x 24 hours x 60 minutes x 60 seconds = 10826956800 seconds in 352 years. After plugging this information into the radioactive decay formula, we get:
N(t) = 1.2 x 106e-2.51×10^-10*10826956800
Therefore, N(t) is 79242.3; 79242.3 atoms will be left in the radioactive isotope in 352 years.
- The Plutonium-238 nucleus has 238 neutrons and 94 protons..
NDT Resource Center. (n.d.). Radiographic Inspection. Retrieved from http://www.ndt-ed.org/GeneralResources/Formula/RTFormula/InverseSquare/InverseSquareLaw.htm
Think Quest. (n.d.). Nuclear Chemistry. Retrieved from http://library.thinkquest.org/10429/low/nuclear/nuclear.htm