At temperature T, the rms speed of an O₂ molecule is v. Temperature is doubled and the oxygen gas dissociates completely into atomic O. If the new rms atomic speed is nv, find n.
Physics · Mixed Chapter
JEE Mains

Question

At temperature T, the rms speed of an O₂ molecule is v. Temperature is doubled and the oxygen gas dissociates completely into atomic O. If the new rms atomic speed is nv, find n.

G1 Physics · Accepted Answer

Step 1 — RMS speed of particles in an ideal gas is v = √(3kT/m). Step 2 — Initially the gas has O₂ molecules with molecular mass m at temperature T. Step 3 — After dissociation into atomic oxygen, the mass per particle is m/2 and the new temperature is 2T. Step 4 — Compare squared speeds: (v₂/v₁)² = [(2T)/(m/2)]/[T/m] = 4. Thus v₂/v₁ = 2 and n = 2. Answer: 2.