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 ______ `xx 10^(-2)` cm.

Answer

To solve the problem, we need to find the wavelength of an electromagnetic wave of frequency 3 GHz in a dielectric medium with a relative electric permittivity of 2.25.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Frequency of the wave, \( f = 3 \text{ GHz} = 3 \times 10^9 \text{ Hz} \)
- Relative permittivity of the medium, \( \epsilon_r = 2.25 \)

2. **Calculate the Speed of Light in the Medium:**
The speed of electromagnetic waves in a medium is given by:
\[ v = \frac{c}{\sqrt{\epsilon_r}} \]
where \( c \) is the speed of light in vacuum, approximately \( c = 3 \times 10^8 \text{ m/s} \).

Substituting the values:
\[ v = \frac{3 \times 10^8}{\sqrt{2.25}} = \frac{3 \times 10^8}{1.5} = 2 \times 10^8 \text{ m/s} \]

3. **Use the Wave Equation to Find Wavelength:**
The relationship between speed, frequency, and wavelength is given by:
\[ v = f \lambda \]
Rearranging this equation to find the wavelength \( \lambda \):
\[ \lambda = \frac{v}{f} \]

Substituting the values we calculated:
\[ \lambda = \frac{2 \times 10^8}{3 \times 10^9} = \frac{2}{3} \times 10^{-1} \text{ m} \]

4. **Convert Wavelength to Centimeters:**
Since \( 1 \text{ m} = 100 \text{ cm} \), we convert the wavelength:
\[ \lambda = \frac{2}{3} \times 10^{-1} \text{ m} = \frac{2}{3} \times 10^{-1} \times 100 \text{ cm} = \frac{200}{3} \text{ cm} \approx 66.67 \text{ cm} \]

5. **Express Wavelength in the Required Format:**
We need to express the wavelength in the form \( xx \times 10^{-2} \text{ cm} \):
\[ 66.67 \text{ cm} = 667 \times 10^{-2} \text{ cm} \]

### Final Answer:
The wavelength of the wave in the medium is approximately \( 667 \times 10^{-2} \text{ cm} \).