What is the nuclear binding energy for uranium-238 in joules? Assume the following:

Question

Mass defect = 3.2008 x 10-27 kilograms
Use E = mc2, with c = 3 x 108 m/s
A.
0.28807 x 10-12 joules
B.
2.8807 x 10-12 joules
C.
2.8807 x 10-10 joules
D.
2.8807 x 10-8 joules
E.
3.2008 x 1027 joules

Answer 1

To find the nuclear binding energy using the given mass defect and Einstein’s equation \(E = mc^2\), we can substitute the mass defect and the speed of light into the equation.

1. Given:

   • Mass defect, \(m = 3.2008 \times 10^{-27}\) kg
   • Speed of light, \(c = 3 \times 10^8\) m/s

2. Applying the equation \(E = mc^2\):

\[ E = (3.2008 \times 10^{-27} \text{ kg}) \times (3 \times 10^{8} \text{ m/s})^2 \]

3. Calculate \(c^2\):

\[ (3 \times 10^{8} \text{ m/s})^2 = 9 \times 10^{16} \text{ m}^2/\text{s}^2 \]

4. Now substitute \(c^2\) back into the energy equation:

\[ E = 3.2008 \times 10^{-27} \text{ kg} \times 9 \times 10^{16} \text{ m}^2/\text{s}^2 \]

5. Calculate \(E\):

\[ E = 3.2008 \times 9 \times 10^{-27 + 16} \] \[ E = 28.8072 \times 10^{-11} \text{ joules} \] \[ E = 2.88072 \times 10^{-10} \text{ joules} \]

To match significant figures, we can round it to \(2.8807 \times 10^{-10}\) joules.

Thus, the correct answer is:

C. \(2.8807 \times 10^{-10}\) joules.