6. Atomic Mass Spectroscopy. Detuubr Figure 7: A velocity selector (left) and a

Question

6. Atomic Mass Spectroscopy. Detuubr Figure 7: A velocity selector (left) and a mass spectrometer (right). (a) Velocity selector: The electric field between two conducting plates, E =-Ek, points vertically downwards as shown in the figure. The magnetic field between the plates, B- Bj is into the page. A charge q enters the region between the plates moving right at a velocity (i) Determine the force on the particle. (ii) At what speed should the particle be injected in order that it undergoes no deflection in passing between the plates? Give your answer in terms of q, E and B. (iii) Particles that are deflected get stuck to the plates. Thus this device functions as a velocity selector. Only particles that travel at the speed calculated in part (ii) emerge from between the plates. (b) Mass spectrometer: To the right of the screen shown in the figure, a uniform magnetic field B points directly into the page. A particle of mass m and charge q moving at a speed v enters this region through a hole in the screen. (i) Describe the subsequent motion of the particle (one or two sentences). (ii) At what distance h should the detector D be placed to ensure that it captures the deflected particle? Give your answer in terms of q, B, m and v. (c) Atomic mass spectroscopy: In order to separate the common isotope of carbon, 12C, from radio carbon, 4C, a carbon sample is vaporized and the vapor atoms are singly ionized. The resulting 12C+ and 4C+ ions are passed through a velocity selector and injected into a mass spectrometer where atoms of the two isotopes are deflected different amounts owing to their mass differential. Thus isotope separation can be performed with high precision but it is a

Explanation / Answer

a

(i) force=-qE(k) +qvB(k)=q(vB-E)k

(ii) for no deflection

Force must be zero

q(vB-E)=0

v=E/B

(b)

(i) motion will be circular with force toward the center of the circle

(ii) h will be diameter of the circle

So h=2mv/qB

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