In a photoelectric tube, the voltage applied is such that the photoelectrons emitted reverse in direction after traveling half the distance. we keep the voltage same but halve the distance, then

Options

A. The photoelectrons reverse the direction at half of the new distance
B. The photoelectrons are just able to reach the other electrode
C. The photoelectrons reverse the direction at one fourth of the new distance
D. The photoelectrons reach the other electrode with some kinetic energy

Answer

To solve the problem, we need to analyze the situation in a photoelectric tube where photoelectrons are emitted and influenced by an electric field. Let's break it down step by step.

### Step 1: Understand the Initial Setup
In the photoelectric tube, we have a metal target where electromagnetic waves (light) are incident. When these waves hit the metal, electrons absorb energy and are emitted from the surface. The emitted electrons have some kinetic energy and start moving towards a positively charged plate.

**Hint:** Remember that photoelectrons are emitted due to the absorption of energy from incident light.

### Step 2: Analyze the Electric Field
The setup includes two plates: one positively charged and the other negatively charged. The electric field is directed from the positive plate to the negative plate. When the photoelectrons are emitted, they experience a force due to this electric field.

**Hint:** The direction of the electric field affects the motion of the electrons.

### Step 3: Motion of Photoelectrons
Initially, the photoelectrons travel towards the positive plate. However, due to the negative charge of the plate they are moving towards, they experience a force in the opposite direction, which slows them down. The problem states that they reverse direction after traveling half the distance.

**Hint:** Consider the effect of the electric field on the kinetic energy of the electrons.

### Step 4: Halving the Distance
Now, we keep the voltage (and thus the electric field strength) the same but halve the distance between the plates. This means the distance the electrons have to travel is reduced.

**Hint:** Think about how reducing the distance affects the time and distance the electrons travel before they are influenced by the electric field.

### Step 5: Analyze the New Situation
Since the electric field strength remains unchanged and the kinetic energy of the emitted electrons is the same, the electrons will still experience the same retardation force. However, because the distance is halved, they will not travel as far before the force acts on them.

**Hint:** The electrons will still experience the same force, but they will have less distance to travel before being affected.

### Step 6: Conclusion
In this new setup, the photoelectrons will just be able to reach the other plate before reversing direction. This means they will travel a shorter distance and will still be influenced by the electric field, causing them to stop and reverse direction after reaching the new position.

**Final Answer:** The photoelectrons will just be able to reach the other plate before reversing direction.

### Summary of Steps:
1. Understand the initial setup of the photoelectric tube.
2. Analyze the electric field created by the charged plates.
3. Consider the motion of the photoelectrons and the effect of the electric field.
4. Halve the distance between the plates while keeping the voltage the same.
5. Conclude that the photoelectrons will just reach the other plate before reversing direction.