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

Binding energy = $$18 \times 10^8$$ J. Find the mass difference between nucleons and the nucleus.

$$E = \Delta m \cdot c^2$$

The binding energy represents the energy equivalent of the mass defect $$\Delta m$$.

$$\Delta m = \frac{E}{c^2} = \frac{18 \times 10^8}{(3 \times 10^8)^2} = \frac{18 \times 10^8}{9 \times 10^{16}} = 2 \times 10^{-8} \text{ kg}$$

$$1 \text{ kg} = 10^9 \; \mu\text{g}$$, so:

$$\Delta m = 2 \times 10^{-8} \times 10^9 = 20 \; \mu\text{g}$$

The correct answer is Option (2): 20 $$\mu$$g.