X-rays, gamma rays and microwaves travelling in vacuum have

Options

A. same wavelength but different velocities
B. same frequency but different velocities
C. same velocity but different wavelentghs
D. same velocity and same frequency

Explanation

To solve the question regarding X-rays, gamma rays, and microwaves traveling in a vacuum, we need to analyze the properties of electromagnetic waves.

### Step-by-Step Solution:

1. **Understanding Electromagnetic Waves**:
- X-rays, gamma rays, and microwaves are all types of electromagnetic waves. They travel through a vacuum at the speed of light, denoted as \( c \).

2. **Speed of Light in Vacuum**:
- In a vacuum, all electromagnetic waves travel at the same speed, which is approximately \( 3 \times 10^8 \) m/s. This is true regardless of the type of electromagnetic wave.

3. **Relationship Between Wavelength and Frequency**:
- The relationship between the speed of light (\( c \)), wavelength (\( \lambda \)), and frequency (\( f \)) is given by the equation:
\[ c = \lambda \times f \]
- This means that if the speed of light is constant, any change in wavelength will result in a corresponding change in frequency.

4. **Comparing X-rays, Gamma Rays, and Microwaves**:
- X-rays and gamma rays have much shorter wavelengths compared to microwaves.
- Gamma rays have the shortest wavelength and highest frequency, followed by X-rays, and then microwaves, which have the longest wavelength and lowest frequency.

5. **Conclusion**:
- Since all three types of waves travel at the same speed in a vacuum, but have different wavelengths and frequencies, the correct statement is that X-rays, gamma rays, and microwaves traveling in vacuum have the **same velocity but different wavelengths and frequencies**.

### Final Answer:
- The correct option is: **same velocity but different wavelength and frequency**.