The photoelectrons emitted from a metal surface:

Options

A. Are all at rest
B. Have the same kinetic energy
C. Have the same momentum
D. Have speeds varying from zero up to certain maximum value

Explanation

To solve the question regarding the characteristics of photoelectrons emitted from a metal surface, we will analyze the properties of these electrons based on the photoelectric effect.

### Step-by-Step Solution:

1. **Understanding the Photoelectric Effect**:
The photoelectric effect occurs when light (photons) strikes a metal surface and causes the emission of electrons. The energy of the incoming photons is absorbed by the electrons.

**Hint**: Recall that the photoelectric effect demonstrates the particle nature of light, where photons can impart energy to electrons.

2. **Energy of Photons**:
According to Planck's law, the energy (E) of a photon is given by the equation:
\[ E = h \nu \]
where \( h \) is Planck's constant and \( \nu \) is the frequency of the light. When photons hit the metal surface, they transfer energy to the electrons.

**Hint**: Remember that the energy of the emitted electrons depends on the frequency of the incident light.

3. **Kinetic Energy of Emitted Electrons**:
The kinetic energy (K.E.) of the emitted electrons can be expressed as:
\[ K.E. = E - \phi \]
where \( E \) is the energy of the incident photon and \( \phi \) is the work function of the metal (the minimum energy required to remove an electron from the metal surface).

**Hint**: The work function is a key factor in determining whether an electron can be emitted.

4. **Distribution of Kinetic Energy**:
Since the energy of the incoming photons is constant (same frequency), the emitted electrons will have varying kinetic energies depending on how much energy they absorbed beyond the work function. This leads to a distribution of kinetic energies among the emitted electrons.

**Hint**: Consider that not all electrons are bound with the same energy; some may be closer to the surface and require less energy to be emitted.

5. **Momentum of Emitted Electrons**:
The momentum of an electron is given by:
\[ p = mv \]
where \( m \) is the mass of the electron and \( v \) is its velocity. Since the emitted electrons have different kinetic energies, they will also have different momenta.

**Hint**: Momentum is directly related to both mass and velocity; if velocities vary, so will the momentum.

6. **Conclusion**:
Based on the analysis, we conclude that:
- The photoelectrons emitted from a metal surface do not all have the same kinetic energy.
- They do not all have the same momentum.
- They have speeds varying from 0 up to a certain maximum value, depending on the energy absorbed from the incident photons.

Therefore, the correct statement is that the photoelectrons have speeds varying from 0 up to a certain maximum value.

**Final Answer**: The correct statement is that the photoelectrons emitted from a metal surface have speeds varying from 0 up to a certain maximum value.