---
title: "A student models an ideal isotope-separation cascade containing uranium hexafluoride gas. The apparatus has \\(5\\) chambers separated by \\(4\\) identical microscopic openings. Gas that effuses through each opening is isolated and used as the feed for the next opening. Each chamber is maintained at \\(400\\ \\text{K}\\), back-effusion is negligible, and only an infinitesimal portion of each feed is transferred.  | Gas species | Molar mass | |—|—:| | \\({}^{235}\\text{U}\\text{F}_6\\text{(g)}\\) | \\(349\\ \\text{g mol}^{-1}\\) | | \\({}^{238}\\text{U}\\text{F}_6\\text{(g)}\\) | \\(352\\ \\text{g mol}^{-1}\\) |  Let \\(R_0\\) be the molecular ratio \\(\\dfrac{n({}^{235}\\text{U}\\text{F}_6)}{n({}^{238}\\text{U}\\text{F}_6)}\\) in the original feed, and let \\(R_4\\) be the ratio in the gas collected after the \\(4\\) effusion stages. According to Graham’s law, what is the value of \\(\\dfrac{R_4}{R_0}\\)?"
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date_modified: "2026-08-21T08:41:05+00:00"
---

# A student models an ideal isotope-separation cascade containing uranium hexafluoride gas. The apparatus has \(5\) chambers separated by \(4\) identical microscopic openings. Gas that effuses through each opening is isolated and used as the feed for the next opening. Each chamber is maintained at \(400\ \text{K}\), back-effusion is negligible, and only an infinitesimal portion of each feed is transferred.

| Gas species | Molar mass |
|—|—:|
| \({}^{235}\text{U}\text{F}_6\text{(g)}\) | \(349\ \text{g mol}^{-1}\) |
| \({}^{238}\text{U}\text{F}_6\text{(g)}\) | \(352\ \text{g mol}^{-1}\) |

Let \(R_0\) be the molecular ratio \(\dfrac{n({}^{235}\text{U}\text{F}_6)}{n({}^{238}\text{U}\text{F}_6)}\) in the original feed, and let \(R_4\) be the ratio in the gas collected after the \(4\) effusion stages. According to Graham’s law, what is the value of \(\dfrac{R_4}{R_0}\)?

A student models an ideal isotope-separation cascade containing uranium hexafluoride gas. The apparatus has \(5\) chambers separated by \(4\) identical microscopic openings. Gas that effuses through each opening is isolated and used as the feed for the next opening. Each chamber is maintained at \(400\ \text{K}\), back-effusion is negligible, and only an infinitesimal portion of each feed is transferred.

| Gas species | Molar mass |
|---|---:|
| \({}^{235}\text{U}\text{F}_6\text{(g)}\) | \(349\ \text{g mol}^{-1}\) |
| \({}^{238}\text{U}\text{F}_6\text{(g)}\) | \(352\ \text{g mol}^{-1}\) |

Let \(R_0\) be the molecular ratio \(\dfrac{n({}^{235}\text{U}\text{F}_6)}{n({}^{238}\text{U}\text{F}_6)}\) in the original feed, and let \(R_4\) be the ratio in the gas collected after the \(4\) effusion stages. According to Graham’s law, what is the value of \(\dfrac{R_4}{R_0}\)?

- **A.** \(\left(\dfrac{352}{349}\right)^{1/2}\approx 1.004\)
- **B.** \(\left(\dfrac{352}{349}\right)^2\approx 1.017\)
- **C.** \(\left(\dfrac{352}{349}\right)^{5/2}\approx 1.022\)
- **D.** \(\left(\dfrac{352}{349}\right)^4\approx 1.035\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120059/*