The number of degrees of freedom for each atom of a monoatomic gas will be

Options

A. a) 3
B. b) 5
C. c) 6
D. d) 1

Explanation

To determine the number of degrees of freedom for each atom of a monoatomic gas, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Degrees of Freedom**:
- Degrees of freedom refer to the number of independent ways in which a system can move. For gas molecules, this includes translational, rotational, and vibrational motions.

2. **Identify the Type of Gas**:
- The question specifies a monoatomic gas. Monoatomic gases consist of single atoms, such as noble gases (e.g., helium, neon).

3. **Determine the Degrees of Freedom Formula**:
- The general formula for calculating the degrees of freedom (f) for a system of particles is given by:
\[ f = 3n - k \]
where:
- \( n \) is the number of particles,
- \( k \) is the number of independent constraints or relationships among the particles.

4. **Substitute Values for Monoatomic Gas**:
- For a monoatomic gas, we have:
- \( n = 1 \) (since we are considering one atom),
- \( k = 0 \) (since there are no constraints for a single atom).
- Plugging these values into the formula gives:
\[ f = 3(1) - 0 = 3 \]

5. **Interpret the Result**:
- The result indicates that a monoatomic gas atom has 3 degrees of freedom, which correspond to its ability to move in three-dimensional space (along the x, y, and z axes). There are no rotational or vibrational degrees of freedom for monoatomic gases.

6. **Conclusion**:
- Therefore, the number of degrees of freedom for each atom of a monoatomic gas is **3**.

### Final Answer:
The number of degrees of freedom for each atom of a monoatomic gas is **3**.

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