Light of wavelength `lambda` strikes a metal surface with intensity `X` and the metal emits `Y` electrons per second of average energy `Z`. What will happen to `Y` and `Z` if `X` is havled?

Options

A. T will be halved
B. Y will double
C. Y will be remain same
D. Z will be halved

Explanation

To solve the problem, we will analyze the effects of halving the intensity of light on the number of emitted electrons (Y) and their average energy (Z).

### Step-by-Step Solution:

1. **Understanding the Relationship Between Intensity and Electron Emission**:
- The intensity (X) of light is directly related to the number of photons striking the metal surface per unit time. The number of emitted electrons (Y) is proportional to the number of incident photons.
- Therefore, if the intensity is halved, the number of incident photons is also halved.

2. **Effect on the Number of Electrons (Y)**:
- Given that the number of emitted electrons is proportional to the intensity of the light, if the intensity is halved (X becomes X/2), the number of emitted electrons (Y) will also be halved.
- Mathematically, if Y is the number of emitted electrons at intensity X, then at intensity X/2, the new number of emitted electrons (Y') will be:
\[ Y' = \frac{Y}{2} \]

3. **Effect on Average Energy of Electrons (Z)**:
- The average energy (Z) of the emitted electrons is determined by the energy of the individual photons, which is given by the equation \(E = \frac{hc}{\lambda}\) (where h is Planck's constant, c is the speed of light, and λ is the wavelength).
- Since the energy of each photon does not change when the intensity is halved (the energy per photon is dependent on the wavelength, which remains constant), the average energy of the emitted electrons (Z) remains the same.
- Therefore, the new average energy (Z') will be:
\[ Z' = Z \]

### Final Results:
- If the intensity (X) is halved:
- The number of emitted electrons (Y) will be halved: \(Y' = \frac{Y}{2}\)
- The average energy of the emitted electrons (Z) will remain unchanged: \(Z' = Z\)