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Vladimir [108]
3 years ago
6

(a) Triply charged uranium-235 and uranium-238 ions are being separated in a mass spectrometer. (The much rarer uranium-235 is u

sed as reactor fuel.) The masses of the ions are 3.90x10—25 kg and 3.95x10—25 kg , respectively, and they travel at 3.00x105 m/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.
Physics
1 answer:
stiv31 [10]3 years ago
3 0

Answer:

(a) 2.5 cm

(b) Yes

Solution:

As per the question:

Mass of Uranium-235 ion, m = 3.95\times 10^{- 25}\ kg

Mass of Uranium- 238, m' = 3.90\times 10^{- 25}\ kg

Velocity, v = 3.00\times 10^{5}\ m/s

Magnetic field, B = 0.250 T

q = 3e

Now,

To calculate the path separation while traversing a semi-circle:

\Delta x = 2(R_{U_{35}} - 2R_{U_{38}})

The radius of the ion in a magnetic field is given by:

R = \frac{mv}{qB}

\Delta x = 2(R_{U_{35}} - 2R_{U_{38}})

\Delta x = 2(\frac{mv}{qB} - \frac{m'v}{qB})

\Delta x = 2(\frac{m - m'}{qB}v)

Now,

By putting suitable values in the above eqn:

\Delta x = 2(\frac{3.95\times 10^{- 25} - 3.90\times 10^{- 25}}{3\times 1.6\times 10^{- 19}\times 0.250}\times 3.00\times 10^{5}) = 2.5\ cm

\Delta x = 1.25\ cm

(b) Since the order of the distance is in cm, thus clearly this distance is sufficiently large enough in practical for the separation of the two uranium isotopes.

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