To find the nuclear binding energy based on the given mass defect, we need to use Einstein's mass-energy equivalence formula, which is [tex]\(E = mc^2\)[/tex].
Here the steps are:
1. Convert the mass defect from atomic mass units (amu) to kilograms (kg):
We use the conversion factor [tex]\(1.6606 \times 10^{-27} \text{ kg/amu}\)[/tex] to convert the mass defect.
[tex]\[\text{Mass defect in kg} = 0.09564 \text{ amu} \times 1.6606 \times 10^{-27} \text{ kg/amu}\][/tex]
2. Square the speed of light:
The speed of light ([tex]\(c\)[/tex]) is [tex]\(3.0 \times 10^8 \text{ m/s}\)[/tex].
[tex]\[c^2 = (3.0 \times 10^8 \text{ m/s})^2\][/tex]
3. Multiply the converted mass defect by the square of the speed of light:
This gives us the nuclear binding energy.
[tex]\[\text{Nuclear binding energy} = (\text{mass defect in kg}) \times c^2\][/tex]
Putting it all together, the correct setup is:
[tex]\[0.09564 \text{ amu} \times \left(1.6606 \times 10^{-27} \text{ kg}\right) / \text{amu} \times \left(3.0 \times 10^8 \text{ m/s}\right)^2\][/tex]
So, the correct setup to calculate the nuclear binding energy is:
[tex]\[0.09564 \text{ amu} \times \left(1.6606 \times 10^{-27} \text{ kg}\right) / \text{amu} \times \left(3.0 \times 10^8 \text{ m/s}\right)^2\][/tex]
