A current passes through a resistor.Let `K_(1)and K_(2)` represent the average kinetic energy of the conduction electrons and the metal ions respectively.

Options

A. (a)`K_(1)ltK_(2)`
B. (b)`K_(1)=K_(2)`
C. (c )`K_(1)gtK_(2)`
D. (d) any of these three may occur.

Answer

To solve the problem, we need to analyze the relationship between the average kinetic energy of conduction electrons (K1) and the average kinetic energy of metal ions (K2) in a resistor when a current flows through it.

### Step-by-Step Solution:

1. **Understanding the Components**:
- In a conductor, there are two main types of particles: conduction electrons (which are free to move and carry current) and metal ions (which are fixed in place within the lattice structure of the metal).

2. **Current Flow in a Resistor**:
- When a current flows through a resistor, the conduction electrons gain energy from the electric field applied across the resistor. This energy is transferred to the conduction electrons, allowing them to drift through the lattice of metal ions.

3. **Kinetic Energy of Particles**:
- The average kinetic energy of conduction electrons (K1) is related to their motion and is influenced by the electric field. The electrons move with a drift speed that is typically much greater than the thermal motion of the metal ions.
- The average kinetic energy of the metal ions (K2) is primarily due to their thermal motion, which is relatively slow compared to the drift speed of the conduction electrons.

4. **Comparison of Kinetic Energies**:
- Since the drift speed of conduction electrons is significantly greater than the thermal speed of the metal ions, we can conclude that the average kinetic energy of the conduction electrons (K1) is greater than that of the metal ions (K2).
- Mathematically, this can be expressed as:
\[ K_1 > K_2 \]

5. **Conclusion**:
- Based on the analysis, we can conclude that the average kinetic energy of conduction electrons (K1) is greater than the average kinetic energy of metal ions (K2). Therefore, the correct option is that \( K_1 > K_2 \).

### Final Answer:
- \( K_1 > K_2 \)