The work function of metal is W and `lamda` is the wavelength of the incident radiation. There is no emission of photoelecrons when

Options

A. `lamdagt(hc)/(W)`
B. `lamda=(hc)/(W)`
C. `lamdalt(hc)/(W)`
D. `lamdale(hc)/(W)`

Explanation

To solve the problem, we need to determine the condition under which there is no emission of photoelectrons when light of wavelength \( \lambda \) is incident on a metal with a work function \( W \).

### Step-by-Step Solution:

1. **Understand the Photoelectric Effect**:
The photoelectric effect states that when light of sufficient energy strikes a metal surface, it can eject electrons from that surface. The energy of the incident photons must be greater than the work function of the metal for photoelectrons to be emitted.

2. **Energy of the Incident Photons**:
The energy \( E \) of a photon can be expressed using the formula:
\[ E = \frac{hc}{\lambda} \]
where \( h \) is Planck's constant and \( c \) is the speed of light.

3. **Condition for No Emission of Photoelectrons**:
For no emission of photoelectrons to occur, the energy of the incident photons must be less than the work function \( W \) of the metal. This can be expressed mathematically as:
\[ E < W \]

4. **Substituting the Expression for Energy**:
Substitute the expression for \( E \) into the inequality:
\[ \frac{hc}{\lambda} < W \]

5. **Rearranging the Inequality**:
To find the condition on \( \lambda \), we rearrange the inequality:
\[ \lambda > \frac{hc}{W} \]

6. **Conclusion**:
Therefore, the condition for no emission of photoelectrons is that the wavelength \( \lambda \) of the incident radiation must be greater than \( \frac{hc}{W} \).

### Final Answer:
The condition for no emission of photoelectrons is:
\[ \lambda > \frac{hc}{W} \]