Question 161: Atoms & Nuclei

Question

Binding energy of a certain nucleus is $$18 	imes 10^8 \mathrm{~J}$$. How much is the difference between total mass of all the nucleons and nuclear mass of the given nucleus:

Accepted Answer

To determine the difference between the total mass of all the nucleons and the nuclear mass of the given nucleus, we need to use the concept of mass-energy equivalence provided by Einstein's famous equation:
$$ E= \Delta m \cdot c^2 $$
where:
E is the binding energy.
$$ \Delta m $$ is the mass defect (difference in mass).
$$ c $$ is the speed of light in vacuum, which is approximately $$3 	imes 10^8 \, 	ext{m/s}$$.
Given:
Binding energy, $$ E = 18 	imes 10^8 \, 	ext{J} $$.
We need to find $$ \Delta m $$, so rearranging the equation:
$$ \Delta m = \frac{E}{c^2} $$
Substitute the given values:
$$ \Delta m = \frac{18 	imes 10^8}{(3 	imes 10^8)^2} $$
Calculate the value:
$$ \Delta m = \frac{18 	imes 10^8}{9 	imes 10^{16}} $$
$$ \Delta m = \frac{18}{9} 	imes 10^{-8} $$
$$ \Delta m = 2 	imes 10^{-8} \, 	ext{kg} $$
To convert the mass from kilograms to micrograms ($$ \mu g $$), we use the conversion factor $$ 1 \, 	ext{kg} = 10^9 \, \mu g $$:
$$ \Delta m = 2 	imes 10^{-8} \, 	ext{kg} 	imes 10^9 \, \frac{\mu g}{	ext{kg}} $$
$$ \Delta m = 2 	imes 10^{1} \, \mu g $$
$$ \Delta m = 20 \, \mu g $$
Therefore, the difference between the total mass of all the nucleons and the nuclear mass of the given nucleus is
20 $$ \mu g $$
.
Option A (20 $$ \mu g $$) is the correct answer.

Answer

20 $$\mu$$g

Answer

2 $$\mu$$g

Answer

10 $$\mu$$g

Answer

0.2 $$\mu$$g

Atoms & Nuclei

Binding energy of a certain nucleus is $18 \times 10^8 \mathrm{~J}$. How much is the difference between total mass of all the nucleons and nuclear mass of the given nucleus:

Choose the correct answer: