Question

What is the rms speed of cesium atoms that have been cooled to a temperature of 100 nk?

Answer 1

Answer : The root mean square speed is, $4.33\times 10^{-3}m/s$

Explanation :

The formula used for root mean square speed is:

$\nu_{rms}=\sqrt{\frac{3kN_AT}{M}}$

where,

$\nu_{rms}$ = root mean square speed

k = Boltzmann’s constant = $1.38\times 10^{-23}J/K$

T = temperature = 100 nK = $100\times 10^{-9}K$

M = atomic mass of cesium = 132.91 g/mole  = 0.13291 kg/mole

$N_A$ = Avogadro’s number = $6.02\times 10^{23}mol^{-1}$

Now put all the given values in the above root mean square speed formula, we get:

$\nu_{rms}=\sqrt{\frac{3\times (1.38\times 10^{-23}J/K)\times (6.02\times 10^{23}mol^{-1})\times (100\times 10^{-9}K)}{0.13291kg/mole}}$

$\nu_{rms}=4.33\times 10^{-3}m/s$

Thus, the root mean square speed is, $4.33\times 10^{-3}m/s$