The slope of the graph drawn between stopping potential and frequency of incident radiation will be

Options

A. `(h)/(c )`
B. he
C. `eh^(2)`
D. `e^(2)h`

Answer

To find the slope of the graph drawn between stopping potential (V₀) and frequency (ν) of incident radiation, we can follow these steps:

### Step 1: Understand the Photoelectric Effect
In the photoelectric effect, when light of frequency ν strikes a metal surface, it imparts energy to electrons. The energy of the incident radiation can be expressed using Planck's equation:
\[ E = hν \]
where \( E \) is the energy of the photon, \( h \) is Planck's constant, and \( ν \) is the frequency of the incident radiation.

### Step 2: Relate Stopping Potential to Energy
The stopping potential (V₀) is the potential needed to stop the most energetic photoelectrons emitted from the surface. The kinetic energy (KE) of the emitted electrons can be expressed as:
\[ KE = eV₀ \]
where \( e \) is the charge of the electron.

### Step 3: Set Up the Energy Equation
According to the conservation of energy, the energy of the incident photon is used to overcome the work function (φ) of the metal and provide kinetic energy to the emitted electrons:
\[ hν = φ + eV₀ \]

### Step 4: Rearranging the Equation
Rearranging the equation gives us:
\[ eV₀ = hν - φ \]
This can be rewritten as:
\[ V₀ = \frac{h}{e}ν - \frac{φ}{e} \]

### Step 5: Identify the Slope
From the equation \( V₀ = \frac{h}{e}ν - \frac{φ}{e} \), we can see that this is in the form of a linear equation \( y = mx + c \), where:
- \( y \) is the stopping potential \( V₀ \)
- \( x \) is the frequency \( ν \)
- \( m \) (the slope) is \( \frac{h}{e} \)

### Conclusion
Thus, the slope of the graph drawn between stopping potential (V₀) and frequency (ν) of incident radiation is:
\[ \text{Slope} = \frac{h}{e} \]

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