Conceptual Question on Mass-Energy Equivalence. #4

Given:

• Unified atomic mass unit, \rm u = 1.6605 \times 10^{ -27} \ kg

To find:

• the amount of energy obtained after converting a nucleus of 14 nucleons completely into free energy?

Since the atomic mass unit is

\rm u = 1.6605 \times 10^{ -27} \ kg

So the rest mass of 14 nucleons is 

\begin{aligned}m_0 &= 14 \times\rm u\\&= 14 \times (1.6605 \times 10^{ -27}\rm \ kg)\\&= 23.247 \times 10^{ -27}\rm \ kg\\\end{aligned}

Therefore, from the mass-energy equivalence, the amount of energy obtained after converting a nucleus of 14 nucleons completely into free energy is

\begin{aligned} E &= m_0 c^2\\ &= (23.247 \times 10^{ -27}\rm \ kg) \times (299792458 \ m/s )^2\\ &= 2.089336164 \times 10^{ -9} \ \rm J\\ &\approx 2.0893 \times 10^{ -9} \ \rm J \\ \end{aligned}