The root mean square speed of molecules of nitrogen gas is v at a certain temperature. When the temperature is doubled, the molecules dissociate into individual atoms. The new rms speed of the atom is:
Correct answer: B. 2v
- A. √2v
- B. 2v
- C. v
- D. 4v
Explanation
When the temperature of nitrogen gas (N₂) is doubled, the root mean square (rms) speed for the N₂ molecules increases by a factor of √2, due to the formula: v rms = √(3kT/m). However, when the molecules dissociate into individual nitrogen atoms, the mass of each atom is half that of an N₂ molecule. Because the rms speed is inversely proportional to the square root of mass, the speed further increases. Thus, the new rms speed of the nitrogen atoms is 2v. Option A (√2v) only accounts for the temperature change, not the dissociation. Option C (v) suggests no change, which is incorrect due to the temperature increase. Option D (4v) exaggerates the effect of temperature and dissociation.
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