Question

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

Answer 1

Answer:

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

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

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

Answer 2

Answer:

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 $10^{-123}$.

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 $10^{-123}$