Which of the following has shortest wavelength, microwave, ultraviolet wave and X-rays?

Answer

To determine which of the given electromagnetic waves (microwave, ultraviolet wave, and X-rays) has the shortest wavelength, we can analyze their respective wavelength ranges based on the electromagnetic spectrum.

### Step-by-Step Solution:

1. **Understand the Electromagnetic Spectrum**: The electromagnetic spectrum is divided into various regions based on wavelength. The order from shortest to longest wavelength is as follows: gamma rays, X-rays, ultraviolet (UV) rays, visible light, infrared rays, microwaves, and radio waves.

2. **Identify Wavelength Ranges**:
- **X-rays**: Wavelengths range from approximately 1 nanometer (1 nm) to 1 picometer (1 pm). This is equivalent to \(10^{-9}\) meters to \(10^{-12}\) meters.
- **Ultraviolet (UV) Waves**: Wavelengths range from about 400 nanometers (400 nm) to 1 nanometer (1 nm). This is equivalent to \(10^{-7}\) meters to \(10^{-9}\) meters.
- **Microwaves**: Wavelengths range from about 1 millimeter (1 mm) to 25 micrometers (25 µm). This is equivalent to \(10^{-3}\) meters to \(25 \times 10^{-6}\) meters.

3. **Compare the Wavelengths**:
- The maximum wavelength of X-rays (1 nm) is shorter than the minimum wavelength of UV rays (400 nm).
- The maximum wavelength of UV rays (400 nm) is significantly longer than the minimum wavelength of microwaves (1 mm).
- Therefore, X-rays have the shortest wavelength compared to UV rays and microwaves.

4. **Conclusion**: Based on the analysis, we can conclude that among microwaves, ultraviolet waves, and X-rays, **X-rays have the shortest wavelength**.

### Final Answer:
**X-rays have the shortest wavelength.**

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