11. (3) The velocity selector in the problem prior to this one is used in a mass

Question

11. (3) The velocity selector in the problem prior to this one is used in a mass spectrometer. Protons (with zero neutrons) are the most common hydrogen nuclei. Some hydrogen isotopes, however, have either one or two neutrons in addition to he proton. If a beam of hydrogen nuclei is shot into a magnetic field of strength 2.0T and the nuclei do a u-turn after which they strike a detector, how far apart will the three isotopes be on the detector surface? Assume both protons and neutrons have a mass of 1.67 x 10 27kg and e 1.60 x 10-19C velacdy Selecter

Explanation / Answer

11. for the given velocity selector

mass of hydrogen nuclei = mp = 1.6*10^-27 kg

mass of 2H = mp + mn = 2mp = 2*1.6*10^-27 kg

mass of 3H = mp + 2mn = 3mp = 3*1.6*10^-27 kg

e = 1.6*10^-19 C

now magnetic field strength = B

speed = v

B = 2 T

hence

radius of hydrogen atom, rh

for 2H = r2

for 3H = r3

hence

mp*v^2/rh = evB

mp*v/rh = eB

rh = mp*v/eB

similiarly

r2 = 2mp*v/eB = 2rh

r3 = 3mp*v/eB = 3rh

rh = 0.000000005v m

so if we know v form the previous problem

distance between 1H and 2H on detector = 2(r2 - rh) = 2rh = 0.00000001v m

and distance between 2H and 3H = 2(r3 - r2) = 0.00000001v m

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