Sound velocity is maximum inA. {{H}_{2}}B. {{N}_{2}}C. HeD. {{O}_{2}}

Velocity of Sound in Gases
The velocity of sound in a medium depends on the properties of that medium, particularly the temperature and the molecular mass. The velocity of sound in a gas is given by the equation:
v=γ⋅R⋅TMv = \sqrt{\frac{\gamma \cdot R \cdot T}{M}}
where:
• vv is the velocity of sound,
• γ\gamma is the adiabatic index (ratio of specific heats),
• RR is the universal gas constant,
• TT is the temperature (in Kelvin),
• MM is the molar mass of the gas.
Since γ\gamma, RR, and TT are constants (or similar for gases under the same conditions), the velocity of sound is inversely proportional to the square root of the molar mass MM.
This means that lighter gases (those with smaller molar mass) allow sound to travel faster, while heavier gases slow down the sound speed.
Analysis of the Options
Let’s look at the molar masses of the gases in the options:
1. A. H2\text{H}_2 (Hydrogen):
o Molar mass of H2\text{H}_2 = 2 g/mol2 \, \text{g/mol}.
o Hydrogen is the lightest of the gases listed, so sound will travel the fastest in hydrogen.
2. B. N2\text{N}_2 (Nitrogen):
o Molar mass of N2\text{N}_2 = 28 g/mol28 \, \text{g/mol}.
o Nitrogen is heavier than hydrogen, so sound will travel slower in nitrogen than in hydrogen.
3. C. He (Helium):
o Molar mass of He = 4 g/mol4 \, \text{g/mol}.
o Helium is lighter than nitrogen and oxygen, but heavier than hydrogen, so sound will travel faster in helium than in nitrogen and oxygen but slower than in hydrogen.
4. D. O2\text{O}_2 (Oxygen):
o Molar mass of O2\text{O}_2 = 32 g/mol32 \, \text{g/mol}.
o Oxygen is heavier than hydrogen, helium, and nitrogen, so sound will travel slower in oxygen than in the other gases listed.
Conclusion:
The velocity of sound is maximum in the lightest gas, which is Hydrogen (H2_2).
Thus, the correct answer is: A. H2\text{H}_2.