In an experiment on the photoelectric effect, an evecuated photocell with a pure metal cothode is used. Which graph best represents the variation of B, the minimum potential defference needed to prevent current from flowing, when x, the frequency of the incident light, is varied?

Options

A.
B.
C.
D.

Explanation

To solve the problem regarding the variation of the minimum potential difference (B) needed to prevent current from flowing in a photoelectric effect experiment as the frequency (x) of the incident light is varied, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Photoelectric Effect**:
The photoelectric effect states that when light of sufficient frequency shines on a metal surface, it can eject electrons from that surface. The energy of the incident photons is given by \(E = hf\), where \(h\) is Planck's constant and \(f\) is the frequency of the incident light.

**Hint**: Remember that the energy of the incident photon is directly proportional to its frequency.

2. **Work Function and Kinetic Energy**:
The energy of the incident photon must overcome the work function (\(\phi\)) of the metal to release an electron. The equation can be expressed as:
\[ hf = \phi + KE_{max} \]
where \(KE_{max}\) is the maximum kinetic energy of the emitted electrons.

3. **Relating Potential Difference to Kinetic Energy**:
The maximum kinetic energy of the emitted electrons can also be expressed in terms of the potential difference (V) as:
\[ KE_{max} = eV \]
where \(e\) is the charge of an electron. Therefore, we can rewrite the equation as:
\[ hf = \phi + eV \]

4. **Rearranging the Equation**:
Rearranging the equation gives us:
\[ V = \frac{hf - \phi}{e} \]
This shows that the potential difference (V) is a linear function of the frequency (f).

5. **Identifying the Minimum Potential Difference**:
The minimum potential difference (B) needed to prevent current from flowing occurs when \(hf = \phi\). Thus, if we set \(V = 0\), we find that:
\[ 0 = \frac{hf - \phi}{e} \implies hf = \phi \implies f = \frac{\phi}{h} \]
This indicates that there is a threshold frequency (\(f_0 = \frac{\phi}{h}\)) below which no photoelectrons are emitted.

6. **Graphical Representation**:
The graph of B (potential difference) versus x (frequency) will be a straight line with a positive slope, starting from the threshold frequency. Below this frequency, the potential difference will be constant (zero), and above this frequency, it will increase linearly.

7. **Selecting the Correct Graph**:
Based on the above analysis, the graph that best represents this relationship will be a straight line that starts from a point on the frequency axis corresponding to the threshold frequency and continues upward, indicating that as the frequency increases, the minimum potential difference also increases.

### Conclusion:
The correct graph is the one that shows a linear increase in potential difference (B) with increasing frequency (x) after a certain threshold frequency.