Answer
$v_{rms}=9.53\times10^6\frac{m}{s}$
Work Step by Step
The root mean square speed $v_{rms}$ of a molecule can be determined as follows
$v_{rms}=\sqrt\frac{3RT}{M}$....eq(1)
To use this equation, we first have to find molar mass of the electron:
$M=m_e \times N_a$ where $m_e=9.11\times10^{-31Kg}$ and Avogadro's Number $N_a=6.023\times10^{23}$
Molar mass of the electron:$M=9.11\times10^{-31}\times6.023\times10^{23}=5.49\times10^{-7}Kg$
Now substituting these values in eq(1) and solving:
$v_{rms}=\sqrt\frac{3(8.314)(2\times10^6)}{5.49\times10^{-7}}$
$v_{rms}=9.53\times10^6\frac{m}{s}$
