An archeologist wants to separate peculiar 15N+ (mass = 15 {1.67E?27 kg} = 24.9E

Question

An archeologist wants to separate peculiar 15N+ (mass = 15 {1.67E?27 kg} = 24.9E?27 kg) from regular 14N+ (mass = 14 {1.67E?27 kg} = 23.2E?27 kg). The ions are shot horizontally Northward from a +2000 V potential , then enter a 0.5 Tesla (downward) B-field . . . . a) how fast are the 15N+ moving? how fast are the 14N+ moving? . . . b) what magnetic Force (strength & direction) is applied to the 15N+ , where they first enter the B-field? ... what F is applied to the 15N+ ? . . . c) what is the radius of the (semicircular) path that the 15N+ travel along, in this B-field ? radius for the 14N+ ? . . . d) calculate the % difference in these radii ... how does that compare with (15-14)/15 = 6.6 % ? Please show any work so I can understand how you got to the answer! Thanks!

Explanation / Answer

a) q V = 1/2 mv^2
for 15:
1.6E-19*2000 = 0.5*15*1.67E-27*v^2
v=159840 m/s
for 14:
1.6E-19*2000 = 0.5*14*1.67E-27*v^2
v=165450 m/s

b) for 15:
F = q v B = 1.6E-19*159840*0.5=1.28E-14 N
for 14:
F=1.6E-19*165450*0.5=1.32E-14 N

c) for 15:
F = mv^2/r
1.28E-14 = 15*1.67E-27*(159840)^2/r
r=0.05 m

for 14:
1.32E-14 = 14*1.67E-27*(165450)^2/r
r=0.0485 m

d) (0.05-0.0485)/0.05=0.03 = 3%

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