Two electrons starting from rest are accelerated by equal potential difference.

Options

A. they will not have same kinetic energy
B. they will have same linear momentum
C. they will not have same de-Broglie wave length
D. None of these correct

Explanation

To solve the problem of two electrons starting from rest and being accelerated by equal potential differences, we will analyze the situation step by step.

### Step 1: Understanding the Kinetic Energy
When an electron is accelerated through a potential difference \( V \), it gains kinetic energy given by the equation:
\[ KE = eV \]
where \( e \) is the charge of the electron. Since both electrons are accelerated through the same potential difference, they will have the same kinetic energy.

### Step 2: Analyzing Linear Momentum
The linear momentum \( p \) of an electron can be expressed as:
\[ p = mv \]
where \( m \) is the mass of the electron and \( v \) is its velocity. Since both electrons have the same charge and are accelerated through the same potential difference, they will have the same kinetic energy. However, the velocity of each electron can be different depending on their mass and the direction of their motion. Therefore, while the magnitudes of their momenta can be the same, the directions can differ.

### Step 3: De Broglie Wavelength
The de Broglie wavelength \( \lambda \) of a particle is given by:
\[ \lambda = \frac{h}{mv} \]
where \( h \) is Planck's constant. Since both electrons have the same mass and are accelerated by the same potential difference, they will have the same velocity (assuming they are identical particles). Thus, they will also have the same de Broglie wavelength.

### Conclusion
Based on the analysis:
- **Option A**: They will have the same kinetic energy - **True**.
- **Option B**: They will have the same linear momentum - **False** (magnitude may be the same, but direction can differ).
- **Option C**: They will have the same de Broglie wavelength - **True**.
- **Option D**: The correct statement is that they will have the same kinetic energy and de Broglie wavelength.

### Final Answer
The correct options are that they will have the same kinetic energy and the same de Broglie wavelength.

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