Question 115: 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: