Light coming from a discharge tube filled with hydrogen falls on the cathode of the photoelectric cell. The work function of the surface of cathode is 4eV Which one of the following values of the anode voltage (in volts ) with respect to the cathode willl likely to make the photoo current zero.

Options

A. (a)`-4`
B. (b)`-4`
C. (c)`-8`
D. (d)`-10`

Answer

To solve the problem step by step, we need to analyze the situation involving the photoelectric effect and the parameters given in the question.

### Step 1: Understand the Photoelectric Effect
The photoelectric effect occurs when light falls on a material (cathode) and causes the emission of electrons. The energy of the incoming photons must be greater than the work function of the material for electrons to be emitted.

### Step 2: Identify Given Values
- Work function of the cathode (Φ) = 4 eV
- Maximum energy of the emitted electrons from hydrogen (E_max) = 13.6 eV

### Step 3: Calculate the Kinetic Energy of Emitted Electrons
The kinetic energy (K.E.) of the emitted electrons can be calculated using the formula:
\[ K.E. = E_{max} - \Phi \]
Substituting the values:
\[ K.E. = 13.6 \, \text{eV} - 4 \, \text{eV} = 9.6 \, \text{eV} \]

### Step 4: Determine the Stopping Potential
The stopping potential (V_s) is the potential difference needed to stop the emitted electrons from reaching the anode. It is equal to the kinetic energy of the electrons:
\[ V_s = K.E. \]
Thus, the stopping potential is:
\[ V_s = 9.6 \, \text{V} \]

### Step 5: Find the Anode Voltage to Make the Photocurrent Zero
To make the photocurrent zero, the anode voltage (V_a) must be equal to the stopping potential but with a negative sign (since we are considering the potential with respect to the cathode):
\[ V_a = -9.6 \, \text{V} \]

### Conclusion
The value of the anode voltage with respect to the cathode that will likely make the photocurrent zero is approximately -10 V (as it is common to round to the nearest whole number).

### Final Answer
The likely value of the anode voltage with respect to the cathode that will make the photocurrent zero is **-10 V**.

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