The mass spectrometer is used on carbon isotopes for carbon dating. If the ^12 C
ID: 1633754 • Letter: T
Question
The mass spectrometer is used on carbon isotopes for carbon dating. If the ^12 C isotope's radius of curvature is 25 cm, and the carbon isotope is singly ionized (q = e), what is the required magnetic field B_2? a. 1.5 T b. 2.5 T c. 14 T d. 25 T e. 120 T Find the separation difference of ^12 C and ^14 C after being bent the half-circle as shown in the figure. (1 atomic mass unit = 1.66 times 10^-27 kg) a. 22 cm b. 12 cm c. 21 cm d. 41 cm e. 60 cm Bonus: What magnetic field, B_2, would be required for a separation distance of 1.0 cm for ^235 U and ^238 U? Assume the same velocity selector speed of 800 km/sec. Is this a realistic setup?Explanation / Answer
radius of curvature r= mass x velocity /(charge x magnetic field)
so, magnetic field =(mass/charge) x velocity /radius
Given: radius r= 4 cm =0.04 m
mass /charge = 12x 1.67 x 10-27/1.67 x10-19 = 12 x 10-8
velocity =
so magnetic field = 12 x velocity/0.04 = 300 x 10-8 x velocity
If velocity = 4.5 x 106 m/s
then magnetic field = 300 x 10-8 x 4.5 x 106 = 13.5 T
In this case option c is the correct answer.
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