A xenon are lamp is covered with an interference filter that only transmits light of 400 nm wavelength. When the transmitted light strikes a metal surface, a stream of electrons emerges from the metal. If the intensity of the light striking the surface is doubled, then

Options

A. More electrons are emitted in a given time interval
B. The electrons that are emitted are more energetic
C. Both of the above
D. Neither of the above

Answer

To solve the problem, we need to analyze the situation based on the photoelectric effect, which describes how light can eject electrons from a metal surface.

### Step-by-Step Solution:

1. **Understanding the Wavelength and Energy of Photons**:
- The wavelength of the transmitted light is given as 400 nm.
- We can calculate the energy of a single photon using the formula:
\[ E = \frac{hc}{\lambda} \]
where \( h \) is Planck's constant (\( 6.626 \times 10^{-34} \, \text{Js} \)), \( c \) is the speed of light (\( 3 \times 10^8 \, \text{m/s} \)), and \( \lambda \) is the wavelength in meters (400 nm = \( 400 \times 10^{-9} \, \text{m} \)).

2. **Calculating the Energy of a Photon**:
- Substituting the values into the formula:
\[ E = \frac{(6.626 \times 10^{-34} \, \text{Js})(3 \times 10^8 \, \text{m/s})}{400 \times 10^{-9} \, \text{m}} \approx 4.97 \times 10^{-19} \, \text{J} \]

3. **Understanding Intensity and Electron Emission**:
- The intensity of light is related to the number of photons striking the surface per unit time. If the intensity is doubled, the number of photons striking the surface per unit time also doubles.
- According to the photoelectric effect, each photon can eject one electron if it has sufficient energy (greater than the work function of the metal).

4. **Effect of Doubling the Intensity**:
- If the intensity is doubled, the number of emitted electrons will also double, assuming the energy of the photons remains constant and they exceed the work function of the metal.
- Therefore, if originally \( n \) electrons were emitted, now \( 2n \) electrons will be emitted.

5. **Conclusion**:
- The intensity of the light striking the surface is doubled, leading to an increase in the number of emitted electrons, but the energy of the emitted electrons remains the same.

### Final Answer:
When the intensity of the light striking the surface is doubled, **more electrons are emitted in the given time interval**.

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