The correct graph respectivley the relation between energy `(E )` of photoelectrons and frequency `v` of incident light is

Options

A.
B.
C.
D.

Answer

To solve the problem of determining the correct graph that represents the relationship between the energy \( E \) of photoelectrons and the frequency \( v \) of incident light, we can follow these steps:

### Step 1: Understand the Photoelectric Effect
The photoelectric effect states that when light of a certain frequency \( v \) strikes a metal surface, it can eject electrons if the energy of the incident photons is greater than the work function \( \phi \) of the metal. The energy of the photons is given by the equation:
\[ E_{\text{photon}} = h v \]
where \( h \) is Planck's constant.

### Step 2: Relate Photon Energy to Photoelectron Energy
The energy of the emitted photoelectrons \( E \) can be expressed as:
\[ E = h v - \phi \]
This equation shows that the energy of the photoelectrons depends linearly on the frequency of the incident light.

### Step 3: Identify the Threshold Frequency
The threshold frequency \( v_0 \) is defined as the minimum frequency of light required to eject electrons from the metal surface. At this frequency, the energy of the photons is equal to the work function:
\[ h v_0 = \phi \]
Thus, when \( v = v_0 \), the energy \( E \) of the emitted photoelectrons becomes zero:
\[ E = h v_0 - \phi = 0 \]

### Step 4: Analyze the Graph
From the equation \( E = h v - \phi \), we can deduce that:
- The graph of \( E \) versus \( v \) is a straight line with a positive slope of \( h \).
- The line intersects the \( E \)-axis at \( E = -\phi \) when \( v = 0 \).
- The line will pass through the origin (0,0) when \( v = v_0 \).

### Step 5: Choose the Correct Graph
Given the characteristics of the graph:
- It should be a straight line with a positive slope.
- It should intersect the frequency axis at the threshold frequency \( v_0 \) where the energy of the photoelectrons is zero.

Based on these observations, the correct graph is the one that represents a linear relationship starting from the threshold frequency and having a positive slope.

### Conclusion
The correct graph that represents the relationship between the energy \( E \) of photoelectrons and the frequency \( v \) of incident light is a straight line with a positive slope, starting from the point where \( E = 0 \) at the threshold frequency \( v_0 \).

---