The electromagnetic waves travel in a medium at a speed of $$2.0 \times 10^8$$ m s$$^{-1}$$. The relative permeability of the medium is $$1.0$$. The relative permittivity of the medium will be

The speed of electromagnetic waves in a medium is given by:

$$v = \frac{c}{\sqrt{\mu_r \varepsilon_r}}$$

where $$c = 3.0 \times 10^8$$ m/s is the speed of light in vacuum, $$\mu_r$$ is the relative permeability, and $$\varepsilon_r$$ is the relative permittivity.

Given: $$v = 2.0 \times 10^8$$ m/s and $$\mu_r = 1.0$$.

Rearranging:

$$\sqrt{\mu_r \varepsilon_r} = \frac{c}{v}$$

$$\mu_r \varepsilon_r = \frac{c^2}{v^2}$$

$$\varepsilon_r = \frac{c^2}{\mu_r v^2} = \frac{(3.0 \times 10^8)^2}{1.0 \times (2.0 \times 10^8)^2}$$

$$\varepsilon_r = \frac{9.0 \times 10^{16}}{4.0 \times 10^{16}} = \frac{9}{4} = 2.25$$

Hence, the correct answer is Option A.