According to Einstein's photoelectric equation, the plot of the maximum kinetic energy of the emitted photoelectrons from a metal versus frequency of the incident radiation gives a straight line whose slope

Options

A. depends on the intensity of incident radiation.
B. depends on the nature of the metal and also on the intensity of incident radiation.
C. is same for all metals and independent of the intensity of the incident radiation.
D. depends on the nature of the metal.

Explanation

To solve the question regarding the slope of the plot of the maximum kinetic energy of emitted photoelectrons versus the frequency of incident radiation according to Einstein's photoelectric equation, we can follow these steps:

### Step 1: Understand Einstein's Photoelectric Equation
Einstein's photoelectric equation is given by:

\[ E = h\nu = \phi + KE \]

Where:
- \( E \) is the energy of the incident photon,
- \( h \) is Planck's constant,
- \( \nu \) is the frequency of the incident radiation,
- \( \phi \) is the work function of the metal,
- \( KE \) is the maximum kinetic energy of the emitted photoelectrons.

### Step 2: Rearranging the Equation
We can rearrange the equation to express the maximum kinetic energy (\( KE \)) in terms of frequency (\( \nu \)):

\[ KE = h\nu - \phi \]

### Step 3: Identify the Form of the Equation
The equation \( KE = h\nu - \phi \) can be compared to the linear equation of the form \( y = mx + c \), where:
- \( y \) is the maximum kinetic energy (\( KE \)),
- \( x \) is the frequency (\( \nu \)),
- \( m \) (the slope) is \( h \) (Planck's constant),
- \( c \) (the y-intercept) is \(-\phi\) (the negative work function).

### Step 4: Determine the Slope
From the rearranged equation, we see that the slope of the line (when plotting \( KE \) against \( \nu \)) is equal to Planck's constant \( h \).

### Step 5: Conclusion
Thus, the slope of the graph represents Planck's constant (\( h \)).

### Final Answer
The slope of the plot of the maximum kinetic energy of the emitted photoelectrons versus the frequency of the incident radiation is equal to Planck's constant \( h \).

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