The radiation having the least wavelength out of the following options is

Options

A. `gamma` - rays
B. `beta` - rays
C. `alpha` - rays
D. X - rays

Answer

To determine which type of radiation has the least wavelength among the given options (alpha rays, beta rays, gamma rays, and x-rays), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Relationship Between Wavelength and Frequency**:
- The relationship between wavelength (λ) and frequency (ν) is given by the equation:
\[ c = λν \]
where \(c\) is the speed of light. This equation shows that wavelength is inversely proportional to frequency.

2. **Identify the Types of Radiation**:
- The types of radiation we are considering are:
- Alpha rays
- Beta rays
- X-rays
- Gamma rays

3. **Rank the Radiations by Frequency**:
- According to the electromagnetic spectrum, the order of these radiations from lowest frequency (and hence longest wavelength) to highest frequency (and hence shortest wavelength) is:
- Alpha rays (lowest frequency)
- Beta rays
- X-rays
- Gamma rays (highest frequency)

4. **Determine the Corresponding Wavelengths**:
- Since frequency is inversely proportional to wavelength, we can conclude:
- Wavelength of alpha rays > Wavelength of beta rays > Wavelength of x-rays > Wavelength of gamma rays

5. **Identify the Radiation with the Least Wavelength**:
- From the ranking, we see that gamma rays have the highest frequency and therefore the least wavelength.

6. **Conclusion**:
- The radiation with the least wavelength among the given options is **gamma rays**.

### Final Answer:
The radiation having the least wavelength out of the following options is **gamma rays**.

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