What is the RMS speed of a moist particle of mass 10^–12 g at 27°C according to kinetic molecular theory?

$$\begin{gathered} \mathrm{KE}=\frac{1}{2}{\mathrm{mV}}^2 \\ \mathrm{V}=\mathrm{RMS} \mathrm{velocity} \\ \mathrm{KE} \mathrm{per} \mathrm{molecule}=\frac{3\mathrm{RT}}{2\mathrm{N}} \\ \frac{1}{2}{\mathrm{mV}}^2=\frac{3\mathrm{RT}}{2\mathrm{N}} \\ \mathrm{V}=\sqrt{\frac{3\mathrm{RT}}{\mathrm{Nm}}} \\ \mathrm{m}={10}^{-12}\mathrm{g} \\ \mathrm{R}=8.314\times {10}^7\mathrm{erg} \\ \mathrm{T}=300\mathrm{K} \\ \mathrm{V}=\sqrt{\frac{3\times 8.314\times 300}{6.023\times {10}^{23}\times {10}^{-12}}} \\ \mathrm{V}=0.35\mathrm{cm}/\sec \end{gathered}$$