To solve this problem, we'll follow these steps:
1. Identify the Initial and Final Masses:
- The initial mass before the nuclear change is [tex]\(2.3465 \times 10^{-27} \, \text{kg}\)[/tex].
- The final mass after the nuclear change is [tex]\(2.3148 \times 10^{-27} \, \text{kg}\)[/tex].
2. Calculate the Mass Defect:
- The mass defect is the difference between the initial and final masses.
[tex]\[
\text{Mass Defect} = \text{Initial Mass} - \text{Final Mass} = 2.3465 \times 10^{-27} \, \text{kg} - 2.3148 \times 10^{-27} \, \text{kg}
\][/tex]
- Performing the subtraction gives:
[tex]\[
\text{Mass Defect} = 3.17 \times 10^{-29} \, \text{kg}
\][/tex]
3. Calculate the Energy Released Using [tex]\(E=mc^2\)[/tex]:
- The speed of light [tex]\(c\)[/tex] is approximately [tex]\(3 \times 10^8 \, \text{m/s}\)[/tex].
[tex]\[
E = (\text{Mass Defect}) \times (c^2) = 3.17 \times 10^{-29} \, \text{kg} \times (3 \times 10^8 \, \text{m/s})^2
\][/tex]
- Squaring the speed of light:
[tex]\[
(3 \times 10^8 \, \text{m/s})^2 = 9 \times 10^{16} \, \text{m}^2/\text{s}^2
\][/tex]
- Multiplying the mass defect by this value gives:
[tex]\[
E = 3.17 \times 10^{-29} \, \text{kg} \times 9 \times 10^{16} \, \text{m}^2/\text{s}^2 = 2.853 \times 10^{-12} \, \text{J}
\][/tex]
Since the closest answer choice to the calculated result [tex]\(2.853 \times 10^{-12} \, \text{J}\)[/tex] is:
[tex]\[2.85 \times 10^{-12} \, \text{J}\][/tex]
Therefore, the energy released during the nuclear change is:
[tex]\[2.85 \times 10^{-12} \, \text{J}\][/tex]
