The best means of personal protection from radiation for emergency responders is the implementation of three basic principles: time, distance and shielding. Please show your work when answering the following questions:
a. Using the inverse square law of radiation, what Geiger counter reading would you get for a radioactive material when you are 3 feet from the source (assume an initial reading of 6300 R at a distance of 1 foot from the source)?
b. Dr. Brown has a radioisotope source containing 1.2 x 106 (also written as 1.2E+06) atoms of Plutonium-238 in 1985, how many atoms will remain in 352 years?
c. How many protons and neutrons are present in the plutonium-238 nucleus?
a. new reading=6500R*1/9
b. atoms=1.2E6*e^((-.693*352)/thalf)
where thalf is the halflife of P238
c. Protons=atomicnumberPu
Neutrons=238-protons
bobpusrsley my answer is 700 hundred for the question A I just don't know how to show the work can you help me with that please.
a. To calculate the Geiger counter reading using the inverse square law of radiation, we need to consider the fact that radiation intensity decreases with the square of the distance from the source.
The inverse square law of radiation states that the radiation intensity is inversely proportional to the square of the distance from the source. Mathematically, it can be expressed as:
I2 = (D1^2 / D2^2) * I1
Where:
I1 = initial radiation intensity at distance D1
I2 = radiation intensity at distance D2
In this case, we have an initial reading of 6300 R at a distance of 1 foot from the source. We want to find the Geiger counter reading when we are 3 feet from the source. Plugging in the values into the equation, we get:
I2 = (1^2 / 3^2) * 6300
I2 = (1/9) * 6300
I2 ≈ 700 R
Therefore, the Geiger counter reading when you are 3 feet from the source would be approximately 700 R.
b. To determine the number of atoms that will remain in 352 years given an initial number of atoms of Plutonium-238, we need to use the concept of half-life.
The half-life of a radioactive substance is the time it takes for half of the atoms in a sample to decay. For Plutonium-238, the half-life is approximately 88 years.
Using the half-life, we can calculate the fraction of atoms remaining after a certain number of half-lives (n) using the formula:
Fraction remaining = (1/2)^n
In this case, we want to determine the number of atoms remaining after 352 years. We can divide 352 by the half-life of 88 years to find the number of half-lives:
Number of half-lives = 352 / 88 = 4
Now, we can calculate the fraction of atoms remaining:
Fraction remaining = (1/2)^4 = 1/16
Finally, we multiply the fraction remaining by the initial number of atoms to find the number of atoms remaining after 352 years:
Atoms remaining = Fraction remaining * Initial number of atoms
Atoms remaining = (1/16) * 1.2E+06
Atoms remaining = 7.5E+04
Therefore, approximately 75,000 atoms of Plutonium-238 will remain after 352 years.
c. The atomic nucleus of plutonium-238 consists of protons and neutrons. To find the number of protons and neutrons, we can examine the atomic number and mass number of plutonium-238.
Plutonium-238 has an atomic number of 94, which represents the number of protons in the nucleus. The atomic mass of plutonium-238 is approximately 238, which represents the total number of protons and neutrons in the nucleus.
The number of neutrons can be calculated by subtracting the atomic number (protons) from the atomic mass:
Neutrons = Atomic mass - Atomic number
Neutrons = 238 - 94
Neutrons = 144
Therefore, the plutonium-238 nucleus contains 94 protons and 144 neutrons.