When a surface is irradiated with light of wavelength `4950 Å`, a photocurrent appears which vanishes if a retarding potential greater than `0.6 V` is applied across the phototube. When a second source of light is used, it is found that the critical potential is changed to `1.1 V`.

If the photoelectrons (after emission form the source) are subjected to a magnetic field of `10 T`, the two retarding potentials would

Options

A. Uniformly increase
B. Uniformly decrease
C. remain the same
D. none of these

Explanation

To solve the problem, we need to analyze the effect of a magnetic field on the photoelectrons emitted from a surface when irradiated with light. Here's a step-by-step breakdown of the solution:

### Step 1: Understand the Photoelectric Effect
The photoelectric effect states that when light of sufficient energy strikes a material, it can eject electrons from that material. The energy of the incident light is given by the equation:
\[ E = \frac{hc}{\lambda} \]
where:
- \( E \) is the energy of the photon,
- \( h \) is Planck's constant (\(6.626 \times 10^{-34} \, \text{Js}\)),
- \( c \) is the speed of light (\(3 \times 10^8 \, \text{m/s}\)),
- \( \lambda \) is the wavelength of the light.

### Step 2: Calculate the Energy of the Incident Light
Given the wavelength \( \lambda = 4950 \, \text{Å} = 4950 \times 10^{-10} \, \text{m} \):
\[ E = \frac{(6.626 \times 10^{-34} \, \text{Js})(3 \times 10^8 \, \text{m/s})}{4950 \times 10^{-10} \, \text{m}} \]

### Step 3: Determine the Work Function
The maximum kinetic energy (KE) of the emitted electrons can be expressed as:
\[ KE = E - \phi \]
where \( \phi \) is the work function of the material. The retarding potential \( V_0 \) is related to the maximum kinetic energy by:
\[ KE = eV_0 \]
where \( e \) is the charge of an electron (\(1.6 \times 10^{-19} \, \text{C}\)).

### Step 4: Analyze the Effect of the Magnetic Field
When the photoelectrons are subjected to a magnetic field, the magnetic field exerts a force on the moving charged particles (photoelectrons). However, this force does not change the kinetic energy of the electrons; it only affects their trajectory. Therefore, the retarding potential \( V_0 \) remains unchanged.

### Step 5: Conclusion
Since the kinetic energy of the emitted photoelectrons does not change due to the magnetic field, the retarding potentials for both light sources will remain the same.

### Final Answer
The two retarding potentials would **remain the same**.

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