The maximum kinetic energy of photoelectrons emitted from a surface when photons of energy `6 eV` fall on it is `4 eV` . The stopping potential , in volt is

Options

A. 2
B. 4
C. 6
D. 10

Explanation

To find the stopping potential when the maximum kinetic energy of photoelectrons is given, we can use the relationship between kinetic energy and stopping potential. Here’s the step-by-step solution:

### Step 1: Understand the relationship between kinetic energy and stopping potential
The stopping potential (V₀) is related to the maximum kinetic energy (K_max) of the emitted photoelectrons by the equation:
\[ K_{max} = e \cdot V_0 \]
where:
- \( K_{max} \) is the maximum kinetic energy of the photoelectrons,
- \( e \) is the charge of the electron (approximately \( 1.6 \times 10^{-19} \) coulombs),
- \( V_0 \) is the stopping potential in volts.

### Step 2: Substitute the known values
From the problem, we know:
- The maximum kinetic energy \( K_{max} = 4 \, \text{eV} \).

We can express this in joules, but since we are looking for the stopping potential in volts, we can keep it in electron volts (eV) for simplicity.

### Step 3: Rearranging the equation to find stopping potential
Rearranging the equation gives us:
\[ V_0 = \frac{K_{max}}{e} \]
Since \( K_{max} \) is already in eV, we can directly substitute:
\[ V_0 = K_{max} \]

### Step 4: Calculate the stopping potential
Substituting the value of \( K_{max} \):
\[ V_0 = 4 \, \text{eV} \]

### Conclusion
Thus, the stopping potential \( V_0 \) is:
\[ V_0 = 4 \, \text{V} \]

### Final Answer
The stopping potential is **4 volts**.

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