The work function of a metal is 3.4 eV. If the frequency of incident radiation is increased to twice, then the work function of the metal becomes.

Options

A. 3.4 eV
B. 7.2 eV
C. 6.8 eV
D. 1.7 eV

Explanation

To solve the problem, we need to understand the concept of work function and how it relates to the frequency of incident radiation.

### Step-by-Step Solution:

1. **Understanding Work Function**: The work function (φ) of a metal is the minimum energy required to remove an electron from the surface of that metal. In this case, the work function is given as 3.4 eV.

2. **Frequency of Incident Radiation**: The frequency of the incident radiation is initially denoted as f. When the frequency is increased to twice its original value, it becomes 2f.

3. **Energy of Incident Radiation**: The energy (E) of the incident radiation can be calculated using the formula:
\[ E = h \cdot f \]
where h is Planck's constant. When the frequency is doubled, the energy becomes:
\[ E' = h \cdot (2f) = 2h \cdot f \]
This means that the energy of the incident radiation has also doubled.

4. **Work Function is Inherent**: The work function is an inherent property of the material and does not change with the frequency of the incident radiation. It remains constant regardless of how much the frequency is increased.

5. **Conclusion**: Since the work function is a characteristic of the metal, even when the frequency of the incident radiation is increased to twice its original value, the work function remains the same at 3.4 eV.

### Final Answer:
The work function of the metal remains 3.4 eV.