1. Tardigrade
  2. Question
  3. Physics
  4. The Earth’s atmosphere consists primarily of oxygen (21 %) and nitrogen (78 %) . The rms speed of oxygen molecules (O2) in the atmosphere at a certain location is 535 m/s . The rms speed of the nitrogen molecules at this location will be [Given 1 amu=1.66× 10- 27 kg , molecular mass of O2=32 , molecular mass of N2=28 ]

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Q. The Earth’s atmosphere consists primarily of oxygen $\left(21 \%\right)$ and nitrogen $\left(78 \%\right)$ . The rms speed of oxygen molecules $\left(O_{2}\right)$ in the atmosphere at a certain location is $535 \, m/s$ . The rms speed of the nitrogen molecules at this location will be [Given $1 \, amu=1.66\times 10^{- 27} \, kg$ , molecular mass of $O_{2}=32$ , molecular mass of $N_{2}=28$ ]

NTA AbhyasNTA Abhyas 2020Thermodynamics

Solution:

The rms speed of $N_{2},v_{r m s , _{N_{2}}}=\sqrt{\frac{3 R T}{M_{N_{2}}}}$
For $O_{2},v_{rms , _{O_{2}}}=\sqrt{\frac{3 R T}{M_{O_{2}}}}$
Thus,
$\frac{v_{r m s , N_{2}}}{v_{r m s , O_{2}}}=\sqrt{\frac{M_{O_{2}}}{M_{N_{2}}}}=\sqrt{\frac{32}{28}}$
$v_{r m s , N_{2}}=572m/s$