Answer : The root mean square speed is, [tex]4.33\times 10^{-3}m/s[/tex]
Explanation :
The formula used for root mean square speed is:
[tex]\nu_{rms}=\sqrt{\frac{3kN_AT}{M}}[/tex]
where,
[tex]\nu_{rms}[/tex] = root mean square speed
k = Boltzmann’s constant = [tex]1.38\times 10^{-23}J/K[/tex]
T = temperature = 100 nK = [tex]100\times 10^{-9}K[/tex]
M = atomic mass of cesium = 132.91 g/mole = 0.13291 kg/mole
[tex]N_A[/tex] = Avogadro’s number = [tex]6.02\times 10^{23}mol^{-1}[/tex]
Now put all the given values in the above root mean square speed formula, we get:
[tex]\nu_{rms}=\sqrt{\frac{3\times (1.38\times 10^{-23}J/K)\times (6.02\times 10^{23}mol^{-1})\times (100\times 10^{-9}K)}{0.13291kg/mole}}[/tex]
[tex]\nu_{rms}=4.33\times 10^{-3}m/s[/tex]
Thus, the root mean square speed is, [tex]4.33\times 10^{-3}m/s[/tex]
