The E.M. wave with shortest wavelength among following is

Options

A. `ultraviolet rays`
B. `xrays`
C. `gamma rays`
D. `microwaves`

Answer

To determine which electromagnetic (E.M.) wave has the shortest wavelength among ultraviolet rays, X-rays, gamma rays, and microwaves, we can follow these steps:

### Step 1: Understand the relationship between energy and wavelength
The energy of an electromagnetic wave is inversely proportional to its wavelength. This relationship can be expressed using the formula:
\[ E = \frac{hc}{\lambda} \]
where:
- \( E \) is the energy of the wave,
- \( h \) is Planck's constant (\(6.626 \times 10^{-34} \, \text{Js}\)),
- \( c \) is the speed of light (\(3 \times 10^8 \, \text{m/s}\)),
- \( \lambda \) is the wavelength.

### Step 2: Compare the energy of the different waves
- **Ultraviolet rays**: Wavelength is approximately 200 nm to 300 nm.
- **X-rays**: Typically have wavelengths in the range of 0.01 nm to 10 nm.
- **Gamma rays**: Have wavelengths less than 0.01 nm, often in the range of picometers.
- **Microwaves**: Have wavelengths ranging from 1 mm to 1 m.

### Step 3: Identify the wave with the shortest wavelength
From the comparison:
- Ultraviolet rays have wavelengths in the nanometer range (10^-9 m).
- X-rays have wavelengths in the range of 0.01 nm (10^-11 m) to 10 nm (10^-8 m).
- Gamma rays have wavelengths less than 0.01 nm (10^-11 m).
- Microwaves have wavelengths in the millimeter to meter range (10^-3 m to 1 m).

### Conclusion
Since gamma rays have the shortest wavelength (less than 0.01 nm), they are the E.M. wave with the shortest wavelength among the options provided.

### Final Answer
**Gamma rays** have the shortest wavelength among ultraviolet rays, X-rays, and microwaves.

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