The electromagnetic wave having the shortest wavelength is

Options

A. X-rays
B. `gamma`-rays
C. infrared rays
D. microwaves

Explanation

To determine which electromagnetic wave has the shortest wavelength among the given options (X-rays, Gamma rays, Infrared rays, and Microwaves), we can analyze the wavelength ranges of each type of wave:

1. **Identify the Wavelength Ranges**:
- **X-rays**: The wavelength of X-rays ranges from 0.01 to 10 nanometers (nm).
- **Gamma rays**: The wavelength of Gamma rays is less than 10 picometers (pm).
- **Infrared rays**: The wavelength of Infrared rays ranges from 0.78 to 1000 micrometers (µm).
- **Microwaves**: The wavelength of Microwaves ranges from 1 millimeter (mm) to 1 meter (m).

2. **Convert Units for Comparison**:
- Convert all wavelengths to the same unit for easier comparison.
- 1 nanometer (nm) = 10^-9 meters
- 1 picometer (pm) = 10^-12 meters
- 1 micrometer (µm) = 10^-6 meters
- 1 millimeter (mm) = 10^-3 meters

3. **List the Wavelengths in Meters**:
- **X-rays**: 0.01 nm = 1 x 10^-11 m to 10 nm = 1 x 10^-8 m
- **Gamma rays**: < 10 pm = < 1 x 10^-11 m
- **Infrared rays**: 0.78 µm = 7.8 x 10^-7 m to 1000 µm = 1 x 10^-4 m
- **Microwaves**: 1 mm = 1 x 10^-3 m to 1 m = 1 m

4. **Compare the Wavelengths**:
- From the above conversions:
- Gamma rays: < 1 x 10^-11 m
- X-rays: 1 x 10^-11 m to 1 x 10^-8 m
- Infrared rays: 7.8 x 10^-7 m to 1 x 10^-4 m
- Microwaves: 1 x 10^-3 m to 1 m

5. **Conclusion**:
- The shortest wavelength among the given options is that of Gamma rays, which is less than 10 picometers.

**Final Answer**: The electromagnetic wave having the shortest wavelength is **Gamma rays**.