If the wave length of light in an experiment on photo electric effect is doubled keeping the intensity constant

Options

A. The photo electrons may or may not be emitted
B. The stopping potential decreases if electrons are emitted
C. The photo electric current does not change if electrons are emitted
D. All the above

Answer

To solve the question regarding the effect of doubling the wavelength of light in an experiment on the photoelectric effect while keeping the intensity constant, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Photoelectric Effect**: The photoelectric effect occurs when light shines on a material and causes the emission of electrons. The energy of the emitted electrons depends on the frequency (or wavelength) of the incident light.

2. **Energy of Photons**: The energy \( E \) of a photon is given by the equation:
\[ E = \frac{hc}{\lambda} \]
where \( h \) is Planck's constant, \( c \) is the speed of light, and \( \lambda \) is the wavelength of the light.

3. **Doubling the Wavelength**: If the wavelength is doubled, we have:
\[ \lambda' = 2\lambda \]
The new energy \( E' \) of the photons becomes:
\[ E' = \frac{hc}{\lambda'} = \frac{hc}{2\lambda} = \frac{1}{2} \left( \frac{hc}{\lambda} \right) = \frac{E}{2} \]
This means that the energy of the photons is halved.

4. **Threshold Frequency**: The photoelectric effect will only occur if the energy of the photons is greater than the work function \( \phi \) of the material:
\[ E \geq \phi \]
If the original wavelength \( \lambda \) was such that \( E = \phi \), then doubling the wavelength (and thus halving the energy) means:
\[ E' = \frac{E}{2} < \phi \]
Therefore, no electrons will be emitted.

5. **Conclusion**: Since the energy of the photons is now less than the work function, no photoelectrons will be emitted when the wavelength is doubled.

### Final Answer:
If the wavelength of light in an experiment on the photoelectric effect is doubled while keeping the intensity constant, no electrons will be emitted because the energy of the photons will be less than the work function of the material.

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