0 3. In a mass spectrometer, singly-ionized atoms or molecules (charge le l) are

Question

0 3. In a mass spectrometer, singly-ionized atoms or molecules (charge le l) are first accelerated by a potential difference V, and then are injected into a region of approximately uniform magnetic field B, where the ions execute a half-circle of the cyclotron orbit. The radius of the half-circle R depends on the ion's mass. You want to distinguish isotopes of helium He and He. The accelerated He ions enter through a small pinhole, and, after they have made the half-circle, can be detected by a detector (black vertical line) with linear pixel resolution of d 2.0 mm. Find the accelerating voltage V needed if the spectrometer uses a magnet with B 0.25 T Tl

Explanation / Answer

for circular motion,

magnetic force = m v^2 / r

q v B = m v^2 / r

r = m v / q B

d = 2(m1 - m2) v / q B

2 x 10^-3 = 2(4 - 3) (1.67 x10^-27) v / (1.6 x 10^-19) (0.25)

v = 2.39 x 10^4 m/s

change in KE = q deltaV

m v^2 /2 = q V

V = 10 Volt

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