Question

If there is a loss of 4.36 x 10-5g of mass in a nuclear reaction, how many kJ of energy would be released? Recall that c = 3 x 108 m/s.

A. 1.45 x 10-13
B. 3.92 x 106
C. 3.92 x 109
D. 3.92 x 1012

Answer 1

The energy released due to a loss of 4.36 x 10^-5g of mass in a nuclear reaction is 3.92 x 10^9 J, or 3.92 x 10^6 kJ, using Einstein's mass-energy equivalence formula E = mc^2.

Step-by-step explanation:

To calculate the energy released in a nuclear reaction due to a loss of mass, we use Einstein's mass-energy equivalence formula E = mc², where E is energy, m is mass, and c is the speed of light. Given the mass loss of 4.36 x 10⁻⁵ g (which is 4.36 x 10⁻⁸ kg, since there are 1000 g in a kg), and the speed of light c = 3 x 10⁸ m/s, we calculate the energy released as follows:

E = (4.36 x 10⁻⁸ kg) x (3 x 10⁸ m/s)² = 3.924 x 10⁹ J, which is 3.92 x 10⁶ kJ (since 1 J is 0.001 kJ). Therefore, the correct answer is C. 3.92 x 10⁹.