Please show work and equations used: An archeologist wants to separate peculiar
ID: 2280268 • Letter: P
Question
Please show work and equations used:
An archeologist wants to separate peculiar 15N+ (mass = 15 {1.67E?27 kg} = 24.9E?27 kg) from regular14N+ (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 the14N+ ?
d) calculate the % difference in these radii ... how does that compare with (15-14)/15 = 6.6 % ?
Explanation / Answer
a) we have
for 15N+ KE= potential*charge = 2000*15*1.6*10^-19 J
m=24.9*10^-27 kg
V=sqrt(2*KE/m) =6.209*10^5 m/s
for 14 N+ KE=potential*charge
m=23.2*10^-27kg
V= sqrt(2KE/m) =6.214*10^5 m/s
b) for 15N+ F=v*B*q = 6.209*10^5 *0.5*15*1.6*10^-19 = 7.45*10^-13 N direction is along west
for 14N+ F=v*B*q=6.96*10^-13 N direction is along west
c) for 15 N+ a= F/m = 2.99*10^13 m/s2
radius is given by r=v^2/a = (6.209*10^5) ^2/2.99*10^13 =12.89 mm
for 14N+ a= F/m = 3*10^13 m/s2
radius,r= (6.214*10^5)^2 /3*10^13 =12.87 mm
d) % diff in radii = (12.89-12.87)/12.89 *100 = 0.155 %
it is very less than 6.6%