Enriching uranium with a mass spectrometer

Electricity and Magnetism Level 2

A rudimentary way to enrich uranium for use in nuclear energy or weaponry is to pass an ionized beam of vaporized uranium through a modified mass spectrometer known as a calutron . Assuming an electronmagnet that produces a magnetic field of magnitude $B = 1\text{ T}$ and a voltage oven rated at a potential difference of $V = 2\text{ kV}$ are available, what is the radius of the path traveled by the uranium-235 being isolated? Assume the beam of vaporized uranium is ionized to a charge of $q = 1.6\times10^{-19}\text{C}.$

1\text{ mm}

10\text{ cm}

10\text{ m}

1 \text{ km}

1 solution

July Thomas
May 6, 2016

Relevant wiki: Lorentz Force Law (Magnetic and Mixed Fields)

The radius of orbit for a particle in a uniform magnetic field is $r=\frac{mv}{qB}.$

The only quantity missing is $v.$ As the particle in a mass spectrometer gains its velocity by passing through the potential difference, use conservation of energy to find an expression of $v$ in terms of the known quantities.

$q\Delta V = \Delta K$ $q\Delta V = \frac12mv^2$ $v=\sqrt{\frac{2q\Delta V}{m}}$

Substitute this into the radius equation above.

$r = \frac{m}{qB}\sqrt{\frac{2q\Delta V}{m}} = \frac{1}{B}\sqrt{\frac{2m\Delta V}{q}} \approx 10\text{ cm}$

Thanks for making this question, I really appreciate it. Just wanted to say that it says nitrogen in the last sentence of the problem which might confuse people a little because I think you mean uranium. Thanks again

Jacob Grays - 3 years, 2 months ago

Thanks for your answer I too got confused with the nitrogen in the last sentence, but you cleared it

Tecno Whizz - 1 year, 1 month ago

Enriching uranium with a mass spectrometer

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