Triply charged uranium-235 and uranium-238 ions are being separated in a mass spectrometer. (The much rarer uranium-235 is used as reactor f

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.

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Gerda 5 months 2021-09-03T06:11:04+00:00 1 Answers 2 views 0

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    2021-09-03T06:12:10+00:00

    Answer:

    0.025\ \text{m}

    Yes

    Explanation:

    m_8 = Mass of uranium 238 ion = 3.95\times 10^{-25}\ \text{kg}

    m_5 = Mass of uranium 235 ion = 3.9\times 10^{-25}\ \text{kg}

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

    q = Charge of triply charged ions = 3\times 1.6\times 10^{-19}\ \text{C}

    B = Magnetic field = 0.25 T

    The force balance is

    \dfrac{mv^2}{r}=qvB\\\Rightarrow r=\dfrac{mv}{qB}

    The difference between the radius of the ions are

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

    Separation is given by

    \Delta d=2\Delta r=2\times 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.

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