Question

The plot of maximum kinetic energy of photo-electrons vs the energy of incident photons above threshold frequency is ________.

• A. an oblique straight line with a positive slope.
• B. an oblique straight line with a negative slope.
• C. an oblique straight line passing through the origin.
• D. an exponential curve.
• E. a polynomial curve of order 2.

Hint:

The slope of a $K_{max}$ vs frequency ($\nu$) graph is always Planck's constant ($h$).

Answer 1

The Correct Option is A

Step 1: Understanding the Concept
This question asks to describe the graphical relationship between the maximum kinetic energy of emitted photoelectrons and the energy of the incident photons. This relationship is explained by Einstein's photoelectric effect equation.
Step 2: Key Formula or Approach
Einstein's photoelectric equation is:
\[ K_{max} = h\nu - \phi \] where:
- \(K_{max}\) is the maximum kinetic energy of the photoelectrons.
- \(h\nu\) is the energy of the incident photon (\(E_{photon}\)).
- \(\phi\) is the work function of the material (the minimum energy required to remove an electron).
We need to analyze the graph of \(K_{max}\) (y-axis) versus \(E_{photon}\) (x-axis). Let \(y = K_{max}\) and \(x = E_{photon}\). The equation becomes:
\[ y = x - \phi \] Step 3: Detailed Explanation
1. Analyze the equation.
The equation \(K_{max} = E_{photon} - \phi\) is in the form of a linear equation, \(y = mx + c\).
- \(y = K_{max}\)
- \(x = E_{photon}\)
- The slope, \(m = 1\).
- The y-intercept, \(c = -\phi\).
2. Describe the graph.
- Since the equation is linear, the plot will be a straight line.
- Since the slope \(m=1\) is positive, it is an oblique straight line with a positive slope. "Oblique" means it is not horizontal or vertical.
- The line does not pass through the origin. Instead, it intercepts the y-axis at a negative value, \(-\phi\).
- The line intercepts the x-axis (where \(K_{max}=0\)) at \(E_{photon} = \phi\). This x-intercept corresponds to the threshold frequency (\(h\nu_{th} = \phi\)). The photoelectric effect only occurs for \(E_{photon}>\phi\).
3. Evaluate the options.
(A) an oblique straight line with a positive slope: Correct. The slope is 1.
(B) an oblique straight line with a negative slope: Incorrect. The slope is positive.
(C) an oblique straight line passing through the origin: Incorrect. The y-intercept is \(-\phi\), which is non-zero.
(D) an exponential curve: Incorrect. The relationship is linear.
(E) a polynomial curve of order 2: Incorrect. The relationship is linear (order 1).
Step 4: Final Answer
The plot is an oblique straight line with a positive slope.