How Does E=mc2 Explain Energy Release in Nuclear Fission?

[bjoyful]

1. Homework Statement [/b]

The overall question is:
For this assignment explain how the E=mc2 equation applies to nuclear fission. In your answer illustrate your explanation with an example, being sure to distinguish between mass and mass number, and explain how a nuclear equation differs from a chemical equation. In addition compare the energy released during fission with energy produced from a typical chemical reaction (such as fossil fuel oxidation). It may be useful for you to consider that the combustion of methane releases 50.1 kJ/g - how much mass is lost to produce 50.1 kJ?

I put it all here so hopefully someone can make sense of my anwer below. I welcome any suggestions!

3. The Attempt at a Solution [/b]

Started by inventing a reaction: 92U235 + 0n1 -> 37Rb90 + 55Cs143 + 3 0n1. (typical of a nuclear fission reaction.) The actual atomic masses of these are:
Rb90 = 89.91481
Cs143 = 142.92732.
2 0n1 = 2.01732
Sum = 234.85945. Now subtract:
U235 = 235.04392 to get
loss = 0.18447. One AMU = 931 Mev, so 171.74 Mev liberated by the fission. Chemical reactions produce energies on the order of a few electron volts.

This is where I stop...do I need a table of energy conversion values to convert AMU per mole to joules per mole, and then do a bit of arithmetic? Thanks for helping me out!

 

[Dick]

You already have the energy released (MeV) per U235 atom. The energy release per mole is that times Avogadro's number. Once you have the result in MeV, you don't need a table. 1 electron volt = 1.60217646 × 10^(-19) joules. I just pasted that out of Google.

 

[Blueshift5]

I can provide a response to the content provided. The equation E=mc2 is a fundamental equation in physics that explains the relationship between energy and mass. It states that the energy (E) of an object is equal to its mass (m) multiplied by the speed of light (c) squared. This equation applies to nuclear fission as it involves the splitting of an atom's nucleus, resulting in a release of energy.

In a nuclear fission reaction, a heavy nucleus, such as uranium-235, is bombarded with a neutron, causing it to split into two lighter nuclei, along with the release of several neutrons and a large amount of energy. This energy is a result of the conversion of a small amount of mass into energy, as described by the equation E=mc2. The mass that is lost in this reaction is known as the mass defect, which is the difference between the mass of the reactants and the mass of the products.

To illustrate this, let's take the example provided in the question: 92U235 + 0n1 -> 37Rb90 + 55Cs143 + 3 0n1. The mass of uranium-235 is 235.04392 amu (atomic mass units), while the total mass of the products is 234.85945 amu. This means that a mass of 0.18447 amu has been lost in the reaction. This mass defect is converted into energy according to the equation E=mc2, resulting in a large amount of energy being released.

It is important to note that in nuclear reactions, the mass number (A) of the reactants and products may be different, but the atomic number (Z) remains the same. This is because nuclear reactions involve changes in the nucleus, while chemical reactions involve changes in the electron arrangement.

Now, let's compare the amount of energy released in a nuclear fission reaction to that of a typical chemical reaction, such as the combustion of methane. The energy released from the combustion of 1 gram of methane is 50.1 kJ. Using the equation E=mc2, we can calculate the mass defect for this reaction, which is equivalent to 5.38 x 10^-11 grams. This is a very small amount compared to the mass defect in a nuclear fission reaction, illustrating the vast difference in energy released between the two types of reactions.

In conclusion, the