The work function of a surface of a photosensitive material is `6.2 eV`. The wavelength of the incident radiation for which the stopping potential is `5 V` lies in the

Options

A. ultraviolet region
B. visible region
C. infrared region
D. X-ray region

Answer

To solve the problem, we will use the photoelectric effect principles and the relevant equations. Here are the steps to find the wavelength of the incident radiation:

### Step 1: Understand the Given Values
- Work function (φ) = 6.2 eV
- Stopping potential (V₀) = 5 V

### Step 2: Calculate Maximum Kinetic Energy (Kmax)
The maximum kinetic energy (Kmax) of the emitted electrons can be calculated using the stopping potential:
\[ K_{max} = e \cdot V_0 \]
Where \( e \) (the charge of an electron) is approximately 1 eV when expressed in electron volts. Thus:
\[ K_{max} = 5 \text{ eV} \]

### Step 3: Use Einstein's Photoelectric Equation
According to Einstein's photoelectric equation:
\[ E_{incident} = \phi + K_{max} \]
Where \( E_{incident} \) is the energy of the incident photons. Substituting the values we have:
\[ E_{incident} = 6.2 \text{ eV} + 5 \text{ eV} = 11.2 \text{ eV} \]

### Step 4: Relate Energy to Wavelength
The energy of a photon can also be expressed in terms of its wavelength (λ) using the equation:
\[ E = \frac{hc}{\lambda} \]
Where:
- \( h \) (Planck's constant) = 4.135667696 × 10⁻¹⁵ eV·s
- \( c \) (speed of light) = 3 × 10¹⁸ Å/s (or 3 × 10¹⁰ cm/s)

We can rearrange this to find the wavelength:
\[ \lambda = \frac{hc}{E} \]

### Step 5: Substitute Values
Now substitute \( E = 11.2 \text{ eV} \) into the equation:
\[ \lambda = \frac{12400 \text{ eV·Å}}{11.2 \text{ eV}} \]

### Step 6: Calculate Wavelength
Calculating the above expression:
\[ \lambda = \frac{12400}{11.2} \approx 1107.14 \text{ Å} \]

### Step 7: Determine the Region of Wavelength
The calculated wavelength is approximately 1107 Å. This wavelength falls within the ultraviolet (UV) region of the electromagnetic spectrum.

### Final Answer
The wavelength of the incident radiation for which the stopping potential is 5 V lies in the ultraviolet region.

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