Thereshold wavelength for sodium is ` 6 xx 10^(-7) m ` .
Then photoemission occurs for light of wavelength ` lambda ` if

Options

A. ` lambda gt 6 xx 10^(-7)` metre
B. `lambda lt 6 xx 10^(-7)`
C. `lambda = 5 xx 10^(14)` metre
D. `lambda = 6 xx 10^(-7)`

Answer

To solve the problem, we need to determine the conditions under which photoemission occurs for sodium when the threshold wavelength is given as \( \lambda_0 = 6 \times 10^{-7} \, \text{m} \).

### Step-by-Step Solution:

1. **Understand the Threshold Wavelength**:
The threshold wavelength (\( \lambda_0 \)) is the maximum wavelength of light that can cause photoemission. For sodium, this is given as \( 6 \times 10^{-7} \, \text{m} \).

2. **Photoelectric Effect Principle**:
According to the photoelectric effect, photoemission occurs when the energy of the incoming photons is greater than or equal to the work function (\( W_0 \)) of the material. The energy of a photon can be expressed using the equation:
\[ E = \frac{hc}{\lambda} \]
where \( E \) is the energy of the photon, \( h \) is Planck's constant, \( c \) is the speed of light, and \( \lambda \) is the wavelength of the light.

3. **Condition for Photoemission**:
For photoemission to occur, the energy of the incoming light must be greater than the work function:
\[ E \geq W_0 \]
This translates to:
\[ \frac{hc}{\lambda} \geq \frac{hc}{\lambda_0} \]
Rearranging gives:
\[ \lambda \leq \lambda_0 \]

4. **Conclusion**:
Therefore, for photoemission to occur, the wavelength \( \lambda \) of the incident light must be less than the threshold wavelength \( \lambda_0 \):
\[ \lambda < 6 \times 10^{-7} \, \text{m} \]

### Final Answer:
Photoemission occurs for light of wavelength \( \lambda \) if \( \lambda < 6 \times 10^{-7} \, \text{m} \).

---