3. Separating Uranium in an Ultra-Centrifuge. Consider uranium gas trapped in a centrifuge of radius R and angular speed o. Assume that the gas rotates with the centrifuge, as it will if there is any interaction coupling the gas molecules to each other and the walls. If these interactions are weak, you may use the internal chemical potential for an ideal gas. In the rotating frame, there is a fictitious force, which leads to an effective potential energy which depends on r and o. Derive an expression for the concentration n(r) of the uranium gas dependent on the radial distance r. How would you use your result to separate uranium isotopes, which have different atomic masses? This is why ultra-centrifuges are sought after by anyone wishing to make nuclear weapons. 3. Separating Uranium in an Ultra-Centrifuge. Consider uranium gas trapped in a centrifuge of radius R and angular speed o. Assume that the gas rotates with the centrifuge, as it will if there is any interaction coupling the gas molecules to each other and the walls. If these interactions are weak, you may use the internal chemical potential for an ideal gas. In the rotating frame, there is a fictitious force, which leads to an effective potential energy which depends on r and o. Derive an expression for the concentration n(r) of the uranium gas dependent on the radial distance r. How would you use your result to separate uranium isotopes, which have different atomic masses? This is why ultra-centrifuges are sought after by anyone wishing to make nuclear weapons