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(a) Singly charged uranium-238 ions are accelerated through a potential differen

ID: 2238114 • Letter: #

Question

(a) Singly charged uranium-238 ions are accelerated through a potential difference of 1.60 kV and enter a uniform magnetic field of 1.90 T directed perpendicular to their velocities. Determine the radius of their circular path. cm (b) Repeat for uranium-235 ions. cm (c) How does the ratio of these path radii depend on the accelerating voltage ?V and on the magnitude of the magnetic field strength B? It is proportional to ?V / B. It is inversely proportional to ?V / B. It is proportional to ?V B. It is inversely proportional to ?V B. It is independent of ?V and B.

Explanation / Answer

q v B = m v^2 / r

r = mv / qB

= (m/qV) sqrt[2qV/m]


r = (1 / B ) sqrt [2mV / q]


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a)


r 238 = (1 / 1.90 ) sqrt [2(238)(1.66 * 10-27)(1.60 * 10^3) / (1.6 * 10-19)]


= 0.0468 m


= 4.68 cm


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b)


r 235 = (1 / 1.90 ) sqrt [2(235)(1.66 * 10-27)(1.60 * 10^3) / (1.6 * 10-19)]


= 0.0465 m


= 4.65 cm