1. Given data

• Frequency of electromagnetic wave: $f = 3\,\text{GHz} = 3\times 10^9\,\text{Hz}$
• Relative permittivity of dielectric medium: $\varepsilon_r = 2.25$

For a non-magnetic dielectric medium, $\mu_r = 1$ so the refractive index is $n = \sqrt{\varepsilon_r} = \sqrt{2.25} = 1.5$

2. Speed of wave in the medium

Speed in medium is $v = \frac{c}{n} = \frac{3\times 10^8}{1.5} = 2\times 10^8\,\text{m/s}$

3. Wavelength in the medium

Using $\lambda = \frac{v}{f}$ we get $\lambda = \frac{2\times 10^8}{3\times 10^9}$ $\lambda = \frac{2}{3}\times 10^{-1}\,\text{m}$ $\lambda = 0.0667\,\text{m}$

4. Convert into cm

Since $1\,\text{m} = 100\,\text{cm}$

$\lambda = 0.0667\times 100 = 6.67\,\text{cm}$

Now write it in the required form: $6.67\,\text{cm} = 667\times 10^{-2}\,\text{cm}$

So the blank is: $\boxed{667}$

5. Comparison with stored answer

Stored correct answer = 667

Our derived answer = 667

They match.