Answer:
number of protons: 94
number of neutrons: 145
239
Pu
94
Explanation:
1) The atomic number, Z, of plutonium is Z = 94, i.e plutonium 94 protons
2) Plutoniun-239 is the isotope with mass number 239.
3) Mass number = number of protons + number of neutrons =>
number of neutrons = mass number - number of protons = 239 - 94 = 145
4) The notation requires that you indicate the symbol of the element with the atomic number (number of protons) and the mass number.
You put the mass number as a superscript at the left side of the symbol and the atomic number as subscript to the left of the symbol.
So, in this case the symbol is Pu, the superscript to the left is 239 and the subscript to the left is 94.
239
Pu
94
Answer: The balanced equation for the given reaction is
.
Explanation:
A chemical equation which contains same number of atoms on both reactant and product side.
For example, 
Here, number of atoms on reactant side are as follows.
Number of atoms on product side are as follows.
To balance this equation, multiply
by 2 on reactant side and multiply
by 2. Hence, the equation will be re-written as follows.

Here, number of atoms on reactant side are as follows.
Number of atoms on product side are as follows.
Now, there are same number of atoms on both reactant and product side. So, this equation is balanced.
Thus, we can conclude that the balanced equation for the given reaction is
.
The answer is indeed carbon dating, but let me explain it to you a little bit better: This is so because Carbon dating is the method that has the determination of the age of an organic matter. That is why we can say that that uses a mathematical equation and the half-life of decay to determine the exact date of a fossil. Hope this clarifies everything