Question

Triply charged uranium-235 and uranium-238 ions are being separated in a mass spectrometer. (The much rarer uranium-235 is used as reactor fuel.) The masses of the ions are 3.90×10⁻²⁵kg and 3.95×10⁻²⁵kg, respectively, and they travel at 2.9×10⁵m/s in a 0.24 T field A What is the separation between their paths in meters when they hit a target after traversing a semicircle?

Answer 1

To determine the separation between the paths of uranium-235 and uranium-238 ions, their individual radii of curvature in the magnetic field are calculated and compared. The separation is twice the difference between these radii, reflecting the different paths they take through the mass spectrometer, which is crucial for uranium enrichment purposes.

Step-by-step explanation:

Separation of Uranium Isotopes in a Mass Spectrometer

To calculate the separation between the paths of triply charged uranium-235 and uranium-238 ions in a mass spectrometer, we need to first determine their radii of curvature when they travel through a magnetic field.

Since both ions have the same charge and are traveling at the same speed, the separation between their paths will be due to the slight difference in their masses.

The radius of curvature r is given by the formula r = mv / (qB), with m being the mass of the ion, v the velocity, q the charge, and B the magnetic field strength.

For uranium-235, the radius r_235 is 3.90 × 10⁻²⁵ kg × 3.00 × 10⁵ m/s / (3 × 1.60 × 10⁻ C × 0.250 T) and for uranium-238, the radius r_238 is 3.95 × 10⁻²⁵ kg × 3.00 × 10⁵ m/s / (3 × 1.60 × 10⁻ C × 0.250 T).

The separation S is then the difference between the diameters, which is twice the difference in the radii.

Using the above formula, the separation can be calculated. Once calculated, it's important to discuss whether the separation seems big enough to be practical for separating uranium-235 from uranium-238—a key step in the process of uranium enrichment.