An electromagnetic wave of frequency 3 GHz enters a dielectric medium of relative electric permittivity 2.25 from vacuum. The wavelength of this wave in that medium will be ______ $$\times 10^{-2}$$ cm.

The frequency of the electromagnetic wave is $$f = 3$$ GHz $$= 3 \times 10^9$$ Hz, and the relative electric permittivity of the dielectric medium is $$\varepsilon_r = 2.25$$. For a non-magnetic dielectric medium ($$\mu_r = 1$$), the speed of the electromagnetic wave in the medium is $$v = \frac{c}{\sqrt{\varepsilon_r}}$$.

Substituting the values: $$v = \frac{3 \times 10^8}{\sqrt{2.25}} = \frac{3 \times 10^8}{1.5} = 2 \times 10^8$$ m s$$^{-1}$$.

The wavelength in the medium is $$\lambda = \frac{v}{f} = \frac{2 \times 10^8}{3 \times 10^9} = \frac{2}{30} = \frac{1}{15}$$ m.

Converting to centimetres: $$\lambda = \frac{1}{15} \times 100 = \frac{100}{15} = 6.667$$ cm $$= 667 \times 10^{-2}$$ cm.

Therefore, the wavelength in the medium is $$667 \times 10^{-2}$$ cm.