Saturday, September 22, 2007
Mass Defect and Binding Energy
If you were given a problem like this: "How much energy is needed to separate two neutrons and two protons from C-12 considering that its actual atomic mass is 12.000", how can you solve it?
1. First the constants are:
1.007825 u - mass of a single proton
1.008665 u - mass of neutrons
2. Determine the atomic number of the element. The atomic number of the element determines the number of protons. In this case, C-12 has an atomic number of 6, thus the protons are 6 and the neutrons are six. (12-6=6).
3. Multiply the number of protons to the constant. (6x1.007825 u). Multiply the number of neutrons to the constant. (6x1.008665 u).
4. Add the two products to get the total mass and subtract it from the actual mass. [12-(6.04695 u+ 6.05199u)=12 u - 12.09894 u= 0.09894u].
5. The difference is the mass defect.
6. The binding energy is the energy needed to separate a particle from the nucleus.
BE= mass defect x 931.5 Mev/u where 931.5 is a constant. (Be= 0.09894u x 931.5MeV/u= 92.16261MeV)
7. The problem wants to separate 4 particles from the nucleus so 92.16 MeV/12=7.68 MeV. Then, 7.68 MeV x 4= 30.72 MeV.
The answer is 30.72 MeV.
Easy, right?
I wanted to learn at 10:17 PM.