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Grace [21]
3 years ago
14

What is the binding energy of a nucleus that has a mass defect of 5.81*10-^29 kg

Chemistry
2 answers:
IrinaVladis [17]3 years ago
7 0

Answer:

Choice A: Approximately 5.23 \times 10^{-29} joules.

Explanation:

Apply the famous mass-energy equivalence equation to find the energy that correspond to the \rm 5.81\times 10^{-29} kilograms of mass.

E = m \cdot c^{2},

where

  • E stands for energy,
  • m stands for mass, and
  • c 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 c?

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, c \approx \rm 3.00\times 10^{8}\;m\cdot s^{-1}.

Apply the mass-energy equivalence:

\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}.

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.)

\rm 1\; J = 1\; N \times 1\; m.

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.)

\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}.

In other words, the mass defect here is also \rm 5.23\times 10^{-12}\; J.

salantis [7]3 years ago
6 0

Answer: 5.23*10^-12 j

Explanation:

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