In a photoelectric effect , the `K.E.` of electrons emitted from the metal surface depends upon

Options

A. intensity of light
B. frequency of incident light
C. velocity of incident light
D. both intensity and velocity of light

Answer

To solve the question about the dependence of the kinetic energy (K.E.) of electrons emitted from a metal surface in the photoelectric effect, we can follow these steps:

### Step 1: Understand the Photoelectric Effect
The photoelectric effect occurs when light (or electromagnetic radiation) hits a metal surface and causes the emission of electrons. The energy of the incoming light is absorbed by the electrons in the metal.

**Hint:** Recall that the photoelectric effect is a phenomenon where light causes the emission of electrons from a material.

### Step 2: Use Einstein's Photoelectric Equation
According to Einstein's photoelectric equation, the maximum kinetic energy (K.E.) of the emitted electrons can be expressed as:
\[ K.E. = E - \phi \]
where:
- \( E \) is the energy of the incident light,
- \( \phi \) is the work function of the metal (the minimum energy required to remove an electron from the surface).

**Hint:** The work function is a property of the metal and does not change with the intensity or frequency of light.

### Step 3: Relate Energy to Frequency
The energy of the incident light can be expressed in terms of its frequency (\( \nu \)):
\[ E = h \nu \]
where \( h \) is Planck's constant. Thus, we can rewrite the kinetic energy equation as:
\[ K.E. = h \nu - \phi \]

**Hint:** Remember that the energy of light is directly proportional to its frequency.

### Step 4: Analyze the Equation
From the equation \( K.E. = h \nu - \phi \), we can see that the kinetic energy of the emitted electrons depends on the frequency of the incident light. If the frequency increases, the kinetic energy of the emitted electrons also increases, provided that the frequency is above the threshold frequency (\( \nu_0 \)).

**Hint:** The threshold frequency is the minimum frequency required to emit electrons from the metal surface.

### Step 5: Conclusion
Based on the analysis, we conclude that the kinetic energy of the emitted electrons depends primarily on the frequency of the incident light, not on its intensity or velocity.

**Final Answer:** The correct option is **B**: the kinetic energy of electrons emitted from the metal surface depends upon the frequency of the incident light.