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:

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