A gas centrifuge is a long hollow cylinder of radius 0.12 m that spins about its own axis, as shown…

Step 1. The pressure law. A thin ring of gas at radius $r$ moves in a circle. The net push from the pressure inside and outside it supplies the centripetal force, so $\dfrac{dp}{dr} = \rho\omega^2 r$. With $\rho = \dfrac{pM}{RT}$:

At the wall $\omega r$ is the wall speed $v_w$.

Step 2. The heavy gas (a). The top line is $0.352\ \text{kg/mol} \times 160000\ \text{m}^2/\text{s}^2 = 56320\ \text{J/mol}$, so $\dfrac{Mv_w^2}{2RT} = \dfrac{56320\ \text{J/mol}}{5321.0\ \text{J/mol}} = 10.585$, so the ratio is $e^{10.585} = 3.95 \times 10^{4}$. Nearly all the gas is pressed against the wall.

Step 3. Separation (b). For each kind the number density follows its own partial pressure. Dividing the two laws,

The lighter molecules gather a little more towards the axis.

Step 4. A better machine (c). Set $\alpha = 1.20$: $v_w^2 = \dfrac{2RT\ln 1.20}{\Delta M} = \dfrac{5321.0 \times 0.1823}{0.003}\ \text{m}^2/\text{s}^2$, so $v_w = 569\ \text{m/s}$.