In a monatomic gas, total degrees of freedom are due to

Options

A. translational motion
B. rotational motion
C. vibrational motion
D. oscillation motion

Answer

To determine the total degrees of freedom in a monatomic gas, we can follow these steps:

### Step 1: Understand the concept of degrees of freedom
Degrees of freedom refer to the number of independent ways in which a system can move or store energy. For gas molecules, these movements can be translational, rotational, or vibrational.

### Step 2: Identify the type of gas
In this case, we are dealing with a monatomic gas. Monatomic gases consist of single atoms, such as noble gases (e.g., helium, neon, argon).

### Step 3: Analyze the motion types for monatomic gases
- **Translational Motion**: Monatomic gas particles can move freely in three-dimensional space. This gives them three degrees of freedom corresponding to movement along the x, y, and z axes.
- **Rotational Motion**: Monatomic gases do not have rotational degrees of freedom because they are single atoms. There are no bonds or structures that allow for rotation.
- **Vibrational Motion**: Similarly, monatomic gases do not exhibit vibrational motion as there are no molecular bonds to vibrate.

### Step 4: Calculate the total degrees of freedom
Since monatomic gases only possess translational motion, the total degrees of freedom can be calculated as:
- Total degrees of freedom = Degrees of freedom due to translational motion + Degrees of freedom due to rotational motion + Degrees of freedom due to vibrational motion
- Total degrees of freedom = 3 (translational) + 0 (rotational) + 0 (vibrational) = 3

### Conclusion
The total degrees of freedom for a monatomic gas is 3, which is solely due to translational motion.

### Final Answer
The total degrees of freedom in a monatomic gas are due to translational motion, which is 3.

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