Average `K.E` of thermal neutron is of the order of (in `KeV`)

Options

A. 3 eV
B. 0.03 eV
C. 3 KeV
D. 3 Mev

Answer

To find the average kinetic energy (K.E) of a thermal neutron in kilo electron volts (KeV), we can follow these steps:

### Step 1: Understand the concept of thermal neutrons
Thermal neutrons are neutrons that are in thermal equilibrium with their surroundings, meaning they have a low kinetic energy, typically comparable to the thermal energy of the surrounding particles.

**Hint:** Recall that thermal energy at room temperature is related to the average kinetic energy of particles.

### Step 2: Use the formula for average kinetic energy
The average kinetic energy (K.E) of a particle in thermal equilibrium can be expressed using the formula:
\[ \text{K.E} = \frac{3}{2} k_B T \]
where \( k_B \) is the Boltzmann constant (\( 8.617 \times 10^{-5} \, \text{eV/K} \)) and \( T \) is the temperature in Kelvin.

**Hint:** Consider the typical room temperature (around 300 K) when calculating the average kinetic energy.

### Step 3: Calculate the average kinetic energy at room temperature
Substituting \( T = 300 \, \text{K} \) into the formula:
\[ \text{K.E} = \frac{3}{2} \times (8.617 \times 10^{-5} \, \text{eV/K}) \times 300 \, \text{K} \]
Calculating this gives:
\[ \text{K.E} = \frac{3}{2} \times 8.617 \times 10^{-5} \times 300 \approx 0.0387 \, \text{eV} \]

**Hint:** Remember to convert the result to KeV by dividing by 1000.

### Step 4: Convert the energy to kilo electron volts
\[ 0.0387 \, \text{eV} = 0.0000387 \, \text{KeV} \approx 0.03 \, \text{KeV} \]

### Conclusion
The average kinetic energy of a thermal neutron is of the order of \( 0.03 \, \text{KeV} \).

**Final Answer:** The average K.E of thermal neutron is of the order of \( 0.03 \, \text{KeV} \).

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