Why does Moon have no atmosphere?

Options

A. it is close to death
B. surface temperature of moon is less
C. the escape velocity of the gas molecules is less than their rms velocity on the moon.
D. the escape velocity of the gas molecules is more then their rms velocity on moon.

Explanation

**Step-by-Step Solution:**

1. **Understanding the Concept of Atmosphere:**
- An atmosphere is a layer of gases surrounding a celestial body. For a body to retain an atmosphere, it must have sufficient gravitational pull to keep gas molecules from escaping into space.

2. **Defining Escape Velocity:**
- Escape velocity is the minimum speed needed for an object to break free from the gravitational attraction of a celestial body. It depends on the mass and radius of the body.

3. **Calculating Escape Velocity:**
- The formula for escape velocity (V_escape) is given by:
\[ V_{escape} = \sqrt{2g \cdot R} \]
where \(g\) is the acceleration due to gravity and \(R\) is the radius of the celestial body.

4. **Understanding Root Mean Square Velocity (VRMS):**
- The root mean square velocity of gas molecules is given by:
\[ V_{RMS} = \sqrt{\frac{3kT}{m}} \]
where \(k\) is Boltzmann's constant, \(T\) is the temperature, and \(m\) is the mass of the gas molecules.

5. **Comparing VRMS and Escape Velocity:**
- For the Moon, the escape velocity is lower than that of Earth due to its smaller mass and radius. However, the VRMS of gas molecules remains constant at a given temperature, regardless of the celestial body.

6. **Conclusion:**
- Since the VRMS of gas molecules on the Moon is greater than the escape velocity, gas molecules can easily escape the Moon's gravitational pull. This is why the Moon does not have a significant atmosphere.

**Final Answer:**
The Moon has no atmosphere because the escape velocity of gas molecules on the Moon is less than their root mean square (VRMS) velocity. This allows gas molecules to escape the Moon's gravitational pull.

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