The Ne atom has 10 times the mass of `H_(2)` molecule. Which of the following statements is true?
I. At `25^(@)C` both of them have the same kinetic energy.
II. Ten moles of `H_(2)` would have the same volume as 1 mole of Ne at same temp. and pressure.
III. One mole of Ne exerts the same pressure as one mole of `H_(2)` at STP.
IV. A `H_(2) ` molecule travels 10 times faster than Ne atom at same temperature.
V. At STP, one litre of Ne has 10 times the density of 1 litre of `H_(2).`

Options

A. II, IV, V
B. I, III, V
C. I, II, III
D. I, II

Explanation

To solve the question regarding the Ne atom and H2 molecule, we will analyze each of the statements provided.

### Step 1: Understanding the Mass Relationship
The mass of one Ne atom is given to be 10 times that of an H2 molecule.
- Mass of H2 molecule = 2 g/mol
- Mass of Ne atom = 20 g/mol
This confirms that the mass of Ne is indeed 10 times that of H2.

### Step 2: Analyzing Statement I
**Statement I:** At 25°C, both of them have the same kinetic energy.
- The kinetic energy (KE) of a gas is given by the formula:
\[ KE = \frac{3}{2} RT \]
- Since R (the gas constant) and T (temperature) are the same for both gases, the kinetic energy will be the same.
- **Conclusion:** Statement I is **True**.

### Step 3: Analyzing Statement II
**Statement II:** Ten moles of H2 would have the same volume as 1 mole of Ne at the same temperature and pressure.
- According to the ideal gas law, the volume (V) can be expressed as:
\[ V = \frac{nRT}{P} \]
- For H2 (10 moles):
\[ V_{H2} = \frac{10RT}{P} \]
- For Ne (1 mole):
\[ V_{Ne} = \frac{1RT}{P} \]
- Since \( V_{H2} \) is 10 times \( V_{Ne} \), they do not have the same volume.
- **Conclusion:** Statement II is **False**.

### Step 4: Analyzing Statement III
**Statement III:** One mole of Ne exerts the same pressure as one mole of H2 at STP.
- At STP (Standard Temperature and Pressure), 1 mole of any ideal gas occupies the same volume (22.4 L) and exerts the same pressure (1 atm).
- Therefore, both gases will exert the same pressure.
- **Conclusion:** Statement III is **True**.

### Step 5: Analyzing Statement IV
**Statement IV:** An H2 molecule travels 10 times faster than a Ne atom at the same temperature.
- The average speed of gas molecules is given by:
\[ v \propto \frac{1}{\sqrt{M}} \]
where M is the molar mass.
- For H2 (M = 2 g/mol) and Ne (M = 20 g/mol):
\[ \frac{v_{H2}}{v_{Ne}} = \sqrt{\frac{M_{Ne}}{M_{H2}}} = \sqrt{\frac{20}{2}} = \sqrt{10} \]
- Therefore, H2 travels faster than Ne, but not 10 times faster; it travels \( \sqrt{10} \) times faster.
- **Conclusion:** Statement IV is **False**.

### Step 6: Analyzing Statement V
**Statement V:** At STP, one liter of Ne has 10 times the density of 1 liter of H2.
- Density (d) is given by:
\[ d = \frac{PM}{RT} \]
- Since pressure (P) and temperature (T) are the same for both gases at STP, the density ratio is directly proportional to their molar masses:
\[ \frac{d_{Ne}}{d_{H2}} = \frac{M_{Ne}}{M_{H2}} = \frac{20}{2} = 10 \]
- Thus, the density of Ne is indeed 10 times that of H2.
- **Conclusion:** Statement V is **True**.

### Final Conclusion
The true statements are I, III, and V. The false statements are II and IV.

### Summary of True Statements:
- I. True
- II. False
- III. True
- IV. False
- V. True