A material of mass 1.0 x 10\(^{-2}\)kg undergoes a fission process which decreases its mass by 0.02 percent. Calculate the amount of energy released in the process. (c = 3.0 x 10\(^{8}\)ms\(^{-1}\))
A
1.8 x 1020J
B
1.8 x 1013J
C
1.8 x 1011J
D
1.8 x 1010J
Verified Correct Answer: C.
Physical Principles & Numerical Solution
To calculate the energy released during the fission process, we can use Einstein's mass-energy equivalence principle, given by the formula:
E = \Deltamc\(^2\)
m = 1.0 x 10\(^{-2}\)kg
c = 3.0 x 10\(^8\)ms\(^{-1}\)
Mass decrease = 0.02%
\Deltam = 0.02% x 1.0 x 10\(^{-2}\) = 2.0\times10\(^{−6}\)kg
E = \Deltamc\(^2\) = 2.0\times10\(^{−6}\) x (3.0 x 10\(^8\))\(^2\) = 1.8\times10\(^{11}\)J
Source: Myschool Past Questions Archive (Record #33856)