To determine how much energy is released if a sample loses 0.001 kg of mass through radioactive decay, we'll use the principle of mass-energy equivalence described by Albert Einstein's famous equation:
[tex]\[ E = mc^2 \][/tex]
Here:
- [tex]\( E \)[/tex] denotes the energy released,
- [tex]\( m \)[/tex] is the mass loss (0.001 kg in this case),
- [tex]\( c \)[/tex] is the speed of light in a vacuum ([tex]\( 3 \times 10^8 \)[/tex] m/s).
Let's go through the steps to calculate this:
1. Identify the given values:
- Mass loss, [tex]\( m = 0.001 \)[/tex] kg
- Speed of light, [tex]\( c = 3 \times 10^8 \)[/tex] m/s
2. Substitute these values into the equation:
[tex]\[
E = (0.001 \, \text{kg}) \times (3 \times 10^8 \, \text{m/s})^2
\][/tex]
3. Simplify the expression inside the parentheses (square the speed of light):
[tex]\[
(3 \times 10^8 \, \text{m/s})^2 = 9 \times 10^{16} \, \text{m}^2/\text{s}^2
\][/tex]
4. Multiply the mass by the squared speed of light:
[tex]\[
E = 0.001 \, \text{kg} \times 9 \times 10^{16} \, \text{m}^2/\text{s}^2
\][/tex]
5. Calculate the product:
[tex]\[
E = 9 \times 10^{13} \, \text{J}
\][/tex]
Therefore, the energy released in this process is:
[tex]\( 9 \times 10^{13} \, \text{J} \)[/tex].
So, the correct answer is:
A. [tex]\( 9 \times 10^{13} \, \text{J} \)[/tex]
