Answer: [tex]v_{rms} =[/tex] 273m/s
Explanation: Root Mean Square Speed of an atom or molecule is the speed of a particle in a gas. It is the average speed a particle in a gas can have.
It can be calculated:
[tex]\frac{1}{2}mv^{2} = \frac{3}{2} k_{B}T[/tex]
[tex]v^{2} = \frac{3k_{B}T}{m}[/tex]
[tex]v = \sqrt{\frac{3k_{B}T}{m}}[/tex]
m is mass of one atom or molecule in kg.
An atom of Arsenic sublimes at 614°C. Converting to Kelvin:
T = 614 + 273 = 887K
Molecular mass of As4 is approximately 0.3kg.
[tex]m = \frac{0.3}{6.10^{23}}[/tex]
[tex]m=5.10^{-25}[/tex]kg
Calculating Root mean square speed :
[tex]v = \sqrt{\frac{3*1.4.10^{-23}*887}{5.10^{-25}}[/tex]
[tex]v = \sqrt{745.08.10^{2}[/tex]
v = 273m/s
The root mean square speed of As4 is approximately 273m/s.
