Respuesta :
Answer:
Choice A: Approximately [tex]5.23 \times 10^{-29}[/tex] joules.
Explanation:
Apply the famous mass-energy equivalence equation to find the energy that correspond to the [tex]\rm 5.81\times 10^{-29}[/tex] kilograms of mass.
[tex]E = m \cdot c^{2}[/tex],
where
- [tex]E[/tex] stands for energy,
- [tex]m[/tex] stands for mass, and
- [tex]c[/tex] is the speed of light in vacuum.
The speed of light in vacuum is a constant. However, finding the right units for this value can simplify the calculations a lot. What should be the unit of [tex]c[/tex]?
The mass given is in the appropriate SI unit:
Mass is in kilograms.
Thus, proceed with the speed of light in SI units. The SI unit for speed is meters per second. For the speed of light, [tex]c \approx \rm 3.00\times 10^{8}\;m\cdot s^{-1}[/tex].
Apply the mass-energy equivalence:
[tex]\begin{aligned} E &= m \cdot c^{2} \\ &= \rm 5.81\times 10^{-29}\; kg \times {\left(3.00\times 10^{8}\; m\cdot s^{-1}\right)}^{2}\\ &\approx \rm 5.23\times 10^{-12}\;kg\cdot m^{2}\cdot s^{-2} \end{aligned}[/tex].
The unit of energy is not in joules. Don't be alerted. Consider the definition of a joule of energy. One joule is the work done on an object when a force of one newton acts on the object in the direction of the force through the distance of one meter. (English Wikipedia.)
[tex]\rm 1\; J = 1\; N \times 1\; m[/tex].
However, a force of one newton is defined as the force required to accelerated an object with a mass of one kilogram (not gram) at a rate of one meter per second squared. (English Wikipedia.)
[tex]\begin{aligned}\rm 1\; J &= \rm 1\; N \times 1\; m\\ & = \rm \left(1\; kg\times 1\; m\cdot s^{-2}\right)\times 1\; m\\ &= \rm 1\; kg \cdot m^{2}\cdot s^{-2}\end{aligned}[/tex].
In other words, the mass defect here is also [tex]\rm 5.23\times 10^{-12}\; J[/tex].
