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 need to analyze the relationship between the energy of the incident photons and the work function of the metal. Here’s a step-by-step breakdown:

### Step 1: Understand the Photoelectric Effect
The photoelectric effect describes the phenomenon where electrons are emitted from a metal surface when it is exposed to light (photons). The energy of the emitted electrons depends on the energy of the incident photons.

### Step 2: Write the Energy Equation
According to Einstein's photoelectric equation, the energy \( E \) of the incident photon is given by:
\[ E = h \mu \]
where:
- \( h \) is Planck's constant,
- \( \mu \) is the frequency of the incident light.

### Step 3: Relate Photon Energy to Electron Energy
When a photon strikes the metal surface, part of its energy is used to overcome the work function \( \phi \) of the metal, which is the minimum energy required to remove an electron from the surface. The remaining energy is converted into the kinetic energy of the emitted electron. This can be expressed as:
\[ E = \phi + KE \]
where \( KE \) is the kinetic energy of the emitted electron.

### Step 4: Rearranging the Equation
From the above relationship, we can express the kinetic energy of the most energetic photoelectron as:
\[ KE = h \mu - \phi \]
This shows that the kinetic energy of the emitted electrons depends on the frequency of the incident light and the work function of the metal.

### Step 5: Identify Dependencies
The work function \( \phi \) can be expressed in terms of the threshold frequency \( \mu_0 \):
\[ \phi = h \mu_0 \]
Thus, substituting this into the kinetic energy equation gives:
\[ KE = h \mu - h \mu_0 \]
This indicates that the energy of the most energetic photoelectrons depends on:
- The frequency \( \mu \) of the incident light,
- The work function \( \phi \) of the metal.

### Conclusion
Therefore, the energy of the most energetic photoelectrons emitted from a metal target depends on the frequency of the incident light and the work function of the metal.

### Final Answer
The energy of the most energetic photoelectrons emitted from a metal target depends upon the frequency of the incident light and the work function of the metal.

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