\(v_{rms}=\sqrt{\frac{3RT}{M}}=\sqrt{\frac{3(8.31J/mol \cdot K)(1000K)}{0.004}=2497m/s}\)

\(\frac{\lambda'}{\lambda}=1-\frac{v}{c}\)

\(\lambda'-\lambda=\Delta \lambda=\frac{v}{c} \lambda\)

\(\Delta \lambda=\frac{2497}{3*10^8}(706.52nm)=0.0059nm\)

doppler width \(2 \Delta \lambda=0.012nm\)