The threshold frequency for a metallic surface corresponds to an energy of `6.2eV` and the stopping potential for a radiation incident on this surface is `5 V` . The incident radiation lies in

Options

A. ultra - violet region
B. infra - red region
C. visible region
D. x - ray region

Answer

To solve the problem, we will use the photoelectric effect formula and the given data to find the wavelength of the incident radiation. Then, we will determine the region of the electromagnetic spectrum to which this wavelength belongs.

### Step-by-Step Solution:

1. **Understand the Given Data:**
- Threshold energy (work function, \( \Phi \)) = 6.2 eV
- Stopping potential (\( V_0 \)) = 5 V

2. **Use the Photoelectric Effect Formula:**
The formula relating the energy of the incident photons to the work function and stopping potential is:
\[ E = \Phi + eV_0 \]
where \( E \) is the energy of the incident photons, \( \Phi \) is the work function, and \( eV_0 \) is the energy corresponding to the stopping potential.

3. **Convert the Work Function and Stopping Potential to Energy:**
The energy due to the stopping potential can be calculated as:
\[ eV_0 = 5 \text{ eV} \]
Therefore, the total energy of the incident photons is:
\[ E = \Phi + eV_0 = 6.2 \text{ eV} + 5 \text{ eV} = 11.2 \text{ eV} \]

4. **Relate Energy to Wavelength:**
The energy of a photon can also be expressed in terms of its wavelength (\( \lambda \)) using the equation:
\[ E = \frac{hc}{\lambda} \]
where \( h \) is Planck's constant (\( 4.1357 \times 10^{-15} \text{ eV s} \)) and \( c \) is the speed of light (\( 3 \times 10^8 \text{ m/s} \)).

5. **Rearranging for Wavelength:**
From the equation above, we can rearrange to find the wavelength:
\[ \lambda = \frac{hc}{E} \]

6. **Substituting Values:**
Substituting the values of \( h \), \( c \), and \( E \):
\[ \lambda = \frac{(4.1357 \times 10^{-15} \text{ eV s})(3 \times 10^8 \text{ m/s})}{11.2 \text{ eV}} \]

7. **Calculating Wavelength:**
\[ \lambda = \frac{1.24071 \times 10^{-6} \text{ m eV}}{11.2 \text{ eV}} \approx 1.107 \times 10^{-7} \text{ m} = 110.7 \text{ nm} \]

8. **Determine the Region of the Electromagnetic Spectrum:**
The calculated wavelength of approximately 110.7 nm falls within the ultraviolet (UV) region of the electromagnetic spectrum.

### Conclusion:
Thus, the incident radiation lies in the **ultraviolet region**.