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 3.90×10−25kg3.90×10−25kg and 3.95×10−25kg,3.95×10−25kg, respectively, and they travel at 3.0×105m/s3.0×105m/s in a 0.250-T field. What is the separation between their paths when they hit a target after traversing a semicircle? (b) Discuss whether this distance between their paths seems to be big enough to be practical in the separation of uranium-235 from uranium-238.

Answer 1

`0.025\ \text{m}`

Yes

Step-by-step explanation:

`m_8` = Mass of uranium 238 ion =
`3.95* 10^(-25)\ \text{kg}`

`m_5` = Mass of uranium 235 ion =
`3.9* 10^(-25)\ \text{kg}`

v = Velocity of ions =
`3* 10^5\ \text{m/s}`

q = Charge of triply charged ions =
`3* 1.6* 10^(-19)\ \text{C}`

B = Magnetic field = 0.25 T

The force balance is

`(mv^2)/(r)=qvB\\\Rightarrow r=(mv)/(qB)`

The difference between the radius of the ions are

`\Delta r=(m_8-m_5)(v)/(qB)\\\Rightarrow \Delta r=((3.95* 10^(-25)-3.9* 10^(-25))* 3* 10^5)/(3* 1.6* 10^(-19)* 0.25)\\\Rightarrow \Delta r=0.0125\ \text{m}`

Separation is given by

`\Delta d=2\Delta r=2* 0.0125\\\Rightarrow \Delta d=0.025\ \text{m}`

The separation between their paths when they hit a target after traversing a semicircle is
`0.025\ \text{m}`.

Yes, the distance between the paths is 2.5 cm is a practical separation between as it is easily measurable.