Question

What is the nuclear binding energy of an atom that has a mass defect of 5.0446

Use E = mc2. (Remember: The speed of light is approximately 3.00 x 10 m/s.)
10-29 kg?
5.61 x 10-45 J
1.51 x 10-20
4.54 x 10-123
1.78 x 1045 J

Answer 1

Option C: 4.54 x
`10^(11)` KJ/mol of nuclei

Note: Here in this question option C is not correctly put. It is 4.54 x
`10^(11)` rather than 4.54 x
`10^(-123)`.

Step-by-step explanation:

If mass defect is known, then nuclear binding energy can easily be calculated, here's how:

First step is to convert that mass defect into kg.

Mass defect = 5.0446 amu

Mass defect = 5.0466 x 1.6606 x
`10^(-27)`

Because 1 amu = 1.6606 x
`10^(-27)` Kg.

Mass defect = 8.383 x
`10^(-27)` kg.

Now, we need to find out it's energy equivalent by using following equation:

Using the equation E = mc²:

where c= 3.00 x
`10^(8)` m/s²

E = (8.383 x
`10^(-27)`) x (3.00 x
`10^(8)`)²

E = 7.54 x
`10^(-10)` J this energy is in Joules but nuclear binding energy is usually expressed in KJ/mol of nuclei. Let's convert it:

(7.54 x
`10^(-10)` Joule/nucleus)x(1 kJ/1000 Joule)x(6.022 x
`10^(23)` nuclei/mol) =

4.54 x
`10^(11)` kJ/mol of nuclei .

E = 4.54 x
`10^(11)` kJ/mol of nuclei . So, this is the nuclear binding energy of that atom, which is option C.

Note: Here in this question option C is not correctly put. It is 4.54 x
`10^(11)` rather than 4.54 x
`10^(-123)`

Answer 2

There is no answer that meets the final value of energy.

Maybe C. And you mistakenly put the 3 at the end.

Step-by-step explanation:

Albert Einstein's equation of spatial relativity is the well-known E = mc2, which means that the energy of a body at rest (E) is equal to its mass (m) multiplied by the speed of light (c) at square. Einstein argued that the mass of a body is a measure of its energy content.

Now, if we know the mass of an atom, it is possible to find its energy.

• m = (5.0446 * 10) ∧-29 kg

• c = (3.00 * 10) ∧8 m / s

• E = 5.0446 * 10∧-29 kg * ((3.00x10∧8 m / s) ∧2)

E = 4.54 x10∧-12 k * m∧2 * s∧2

- Knowing that kg * m∧2 * s∧2 is the same as Joules then:

E = 4.54 x10∧-12 J