Photons of energy 5.5 eV are incident on a metal surface. If the stopping potential is 3V, then the work function of the metal will be

Options

A. 2.5 eV
B. 2 eV
C. 8.5 eV
D. 1.5 eV

Explanation

To solve the problem, we need to find the work function of the metal surface when photons of energy 5.5 eV are incident on it, and the stopping potential is 3 V.

### Step-by-Step Solution:

1. **Understand the relationship between photon energy, work function, and stopping potential**:
The energy of the incident photons (E) can be expressed as:
\[ E = W_0 + eV_s \]
where:
- \(E\) is the energy of the photons (5.5 eV),
- \(W_0\) is the work function of the metal,
- \(e\) is the charge of an electron (1 eV/V),
- \(V_s\) is the stopping potential (3 V).

2. **Substitute the known values into the equation**:
We can rearrange the equation to solve for the work function \(W_0\):
\[ W_0 = E - eV_s \]
Substitute \(E = 5.5 \, \text{eV}\) and \(V_s = 3 \, \text{V}\):
\[ W_0 = 5.5 \, \text{eV} - 3 \, \text{eV} \]

3. **Calculate the work function**:
Now, perform the subtraction:
\[ W_0 = 5.5 \, \text{eV} - 3 \, \text{eV} = 2.5 \, \text{eV} \]

4. **Conclusion**:
The work function of the metal is:
\[ W_0 = 2.5 \, \text{eV} \]

### Final Answer:
The work function of the metal is **2.5 eV**.

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