The energy of the most energetic photoelectrons emitted from a metal target depands upon

Options

A. Threhold frequency of the metal
B. Photoelectric work function of the metal
C. Wavelength of the incident radiation
D. All of these

Answer

To solve the question regarding the energy of the most energetic photoelectrons emitted from a metal target, we can break down the explanation into clear steps:

### Step-by-Step Solution

1. **Understanding the Photoelectric Effect**:
The photoelectric effect occurs when light (photons) hits a metal surface and causes the emission of electrons. For this to happen, the photons must have sufficient energy.

**Hint**: Remember that not all photons can eject electrons; they need to meet a certain energy threshold.

2. **Energy of Incident Photons**:
The energy of the incident photons 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 incident light.

**Hint**: The shorter the wavelength, the higher the energy of the photon.

3. **Work Function (\(\phi\))**:
The work function is the minimum energy required to remove an electron from the surface of the metal. It is denoted by \(\phi\).

**Hint**: The work function is a property of the metal and varies from one metal to another.

4. **Kinetic Energy of Photoelectrons**:
When a photon with energy \(E\) strikes the metal, the energy is used to overcome the work function \(\phi\) and the remaining energy is converted into kinetic energy (\(K.E.\)) of the emitted photoelectron. This can be expressed as:
\[ K.E. = E - \phi \]
Substituting the expression for \(E\):
\[ K.E. = \frac{hc}{\lambda} - \phi \]

**Hint**: The kinetic energy of the emitted electrons depends on the difference between the energy of the incident photon and the work function.

5. **Factors Affecting Kinetic Energy**:
From the equation \(K.E. = \frac{hc}{\lambda} - \phi\), we can see that the kinetic energy of the most energetic photoelectrons depends on:
- The wavelength of the incident radiation (\(\lambda\))
- The work function of the metal (\(\phi\))

**Hint**: Both the wavelength of the incoming light and the work function of the metal are crucial in determining the kinetic energy of the emitted electrons.

6. **Conclusion**:
Therefore, the energy of the most energetic photoelectrons emitted from a metal target depends on the wavelength of the incident radiation and the work function of the metal. Thus, the correct answer to the question is that it depends on both of these factors.

**Final Answer**: The energy of the most energetic photoelectrons emitted from a metal target depends on the wavelength of the incident radiation and the work function of the metal.