Question

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

A 5.23*10-^12 J
B 3.15* 10^12 J
C 1.57*10-3 J
D 9.44*10^20 J

Answer 1

Answer: 5.23*10^-12 j

Step-by-step explanation:

Answer 2

Choice A: Approximately
`5.23 * 10^(-29)` joules.

Step-by-step explanation:

Apply the famous mass-energy equivalence equation to find the energy that correspond to the
`\rm 5.81* 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* 10^(8)\;m\cdot s^(-1)`.

Apply the mass-energy equivalence:

`\begin{aligned} E &= m \cdot c^(2) \\ &= \rm 5.81* 10^(-29)\; kg * {\left(3.00* 10^(8)\; m\cdot s^(-1)\right)}^(2)\\ &\approx \rm 5.23* 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 * 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 * 1\; m\\ & = \rm \left(1\; kg* 1\; m\cdot s^(-2)\right)* 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* 10^(-12)\; J`.