Which of the following statement(s) is true

Options

A. The Kinetic energy of an electron is inversely proportional to square of its momentum
B. de-Broglie wavelength associated with a particle is directly proportional to its mass
C. de-Broglie wavelength associated with a particle is directly proportional to square of its velocity
D. The kinetic energy of an electron is directly proportional to accelerating potential

Explanation

To determine which of the statements is true, we will analyze each statement one by one.

### Step 1: Analyze the first statement
**Statement:** Kinetic energy of an electron is inversely proportional to the square of its momentum.

**Analysis:**
- Kinetic energy (KE) is given by the formula:
\[ KE = \frac{p^2}{2m} \]
where \( p \) is momentum and \( m \) is mass.
- Momentum \( p \) is defined as:
\[ p = mv \]
where \( v \) is velocity.
- Therefore, if we express kinetic energy in terms of momentum, we see that kinetic energy is directly proportional to the square of momentum, not inversely.

**Conclusion:** This statement is false.

### Step 2: Analyze the second statement
**Statement:** De Broglie wavelength is directly proportional to its mass.

**Analysis:**
- The De Broglie wavelength (\( \lambda \)) is given by:
\[ \lambda = \frac{h}{p} \]
where \( h \) is Planck's constant and \( p \) is momentum.
- Since momentum \( p = mv \), we can rewrite the wavelength as:
\[ \lambda = \frac{h}{mv} \]
- This shows that the De Broglie wavelength is inversely proportional to mass, not directly proportional.

**Conclusion:** This statement is false.

### Step 3: Analyze the third statement
**Statement:** Kinetic energy of an electron is directly proportional to the accelerating potential.

**Analysis:**
- The kinetic energy gained by an electron when it is accelerated through a potential difference \( V \) is given by:
\[ KE = eV \]
where \( e \) is the charge of the electron.
- This indicates that kinetic energy is directly proportional to the accelerating potential \( V \).

**Conclusion:** This statement is true.

### Step 4: Analyze the fourth statement
**Statement:** The De Broglie wavelength is directly proportional to the square of velocity.

**Analysis:**
- As derived earlier, the De Broglie wavelength is given by:
\[ \lambda = \frac{h}{mv} \]
- This shows that the De Broglie wavelength is inversely proportional to velocity, not directly proportional.

**Conclusion:** This statement is false.

### Final Conclusion
The only true statement among the options provided is that the kinetic energy of an electron is directly proportional to the accelerating potential.