Question

If we completely annihilate a hair of your body that has a mass of $1\mathrm{\mu g}$, how much energy will we get in the process?

• A. $9\times {10}^7\text{J}$
• B. $8\times {10}^7\text{J}$
• C. $9\times {10}^{10}\text{J}$
• D. $8\times {10}^{10}\text{J}$

Answer 1

The correct option is A $9\times {10}^7\text{J}$

Einstein's theory says that if we have a mass $\text{m}$ then it's rest mass energy $\text{E}$ is related to it by $\text{m}=\frac{\text{E}}{{\text{c}}^2}.$ Hence if we annihilate a mass m, according to this equation, the amount of energy that we'll get is ${\text{E = mc}}^2$.
Now, we have a mass of $1\mu \text{g}$.
Hence, the mass energy $\text{E}={10}^{-9}\times (3\times {10}^8)\times (3\times {10}^8)\text{J}$ = $9\times {10}^7\text{J}$