Which is/are correct graph ?

Options

A.
B.
C.
D.

Answer

To determine which graph(s) are correct based on the relationship between kinetic energy and frequency, we can follow these steps:

### Step 1: Understand the Relationship
The kinetic energy (KE) of a photoelectron is given by the equation:
\[ KE = h\nu - \phi \]
where:
- \( KE \) is the kinetic energy,
- \( h \) is Planck's constant,
- \( \nu \) (mu) is the frequency of the incident light,
- \( \phi \) (phi) is the work function of the material.

### Step 2: Rearrange the Equation
We can rearrange the equation to express kinetic energy in terms of frequency:
\[ KE = h\nu - h\nu_0 \]
where \( \nu_0 \) is the threshold frequency (the frequency corresponding to the work function).

### Step 3: Identify the Graph Characteristics
From the rearranged equation, we can see that:
- The equation is linear in the form \( y = mx + c \), where:
- \( y \) is the kinetic energy,
- \( x \) is the frequency,
- \( m \) (the slope) is equal to \( h \) (which is positive),
- \( c \) is the y-intercept (which is negative since it represents the work function).

### Step 4: Analyze the Graphs
Since the slope \( m \) is positive, the graph of kinetic energy versus frequency will be a straight line that rises as frequency increases. The line will intersect the y-axis at a negative value, indicating that kinetic energy is zero when the frequency is equal to the threshold frequency \( \nu_0 \).

### Step 5: Conclusion
All graphs that show a straight line with a positive slope and a negative y-intercept are correct representations of the kinetic energy as a function of frequency. Therefore, if all provided graphs exhibit these characteristics, they are all correct.

### Final Answer
All the graphs with a positive slope and a negative y-intercept are correct.

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