For a photocell, the work function is `phi` and the stopping potential is `V_(s)` . The wavelength of the incident radiation is

Options

A. `(hc)/(phi)`
B. `(hc)/(phi-eV_(s))`
C. `(hc)/(phi+eV_(s))`
D. `(hc)/(ephi+V_(s))`

Explanation

To find the wavelength of the incident radiation for a photocell with a given work function (φ) and stopping potential (Vs), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Photoelectric Effect Equation**:
The maximum kinetic energy (KE_max) of the emitted electrons can be expressed as:
\[ KE_{max} = h\nu - \phi \]
where \( h \) is Planck's constant, \( \nu \) is the frequency of the incident radiation, and \( \phi \) is the work function.

2. **Relate Kinetic Energy to Stopping Potential**:
The maximum kinetic energy can also be expressed in terms of the stopping potential (Vs):
\[ KE_{max} = eV_s \]
where \( e \) is the charge of the electron.

3. **Set the Two Expressions for KE_max Equal**:
Since both expressions represent the maximum kinetic energy, we can set them equal to each other:
\[ eV_s = h\nu - \phi \]

4. **Express Frequency in Terms of Wavelength**:
The frequency \( \nu \) can be related to the wavelength \( \lambda \) using the equation:
\[ \nu = \frac{c}{\lambda} \]
where \( c \) is the speed of light.

5. **Substitute Frequency into the KE Equation**:
Substitute \( \nu \) in the equation from step 3:
\[ eV_s = h\left(\frac{c}{\lambda}\right) - \phi \]

6. **Rearrange the Equation to Solve for Wavelength**:
Rearranging gives:
\[ h\frac{c}{\lambda} = eV_s + \phi \]
Now, isolate \( \lambda \):
\[ \lambda = \frac{hc}{eV_s + \phi} \]

7. **Final Expression for Wavelength**:
Thus, the wavelength of the incident radiation is:
\[ \lambda = \frac{hc}{eV_s + \phi} \]