C Exercise 1916 In a mass spectrometer a singly charged ion

C Exercise 19.16 In a mass spectrometer, a singly charged ion having a particular velocity is selected by using a magnetic field of 0.11T perpendicular to an electric field of 1.5x103 V/m.A magnetic field of this same magnitude is then used to deflect the ion, which moves in a circular path with a radius of 1.1 cm Part A What is the mass of the ion? Express your answer using two significant figures. Submit My Answers Give up Esa

Solution

here,
radius = 1.1 cm = 0.011 m
E = 1.5*10^3 V/m
B = 1.1 T
q = 1.60*10^-19 C

In a Velocity selector Electric field balance with Magnatic Field so parrticle can move in staright line,ThereFore
qE = Bqv

V = E / B
V = (1.5*10^3) / (1.1)
V = 1363.6364 m/s

From Circular Motion Centripital force will be provided by Magnatic Force Therefore We get,

m*V^2/r = q*v*B
solving for mass of particle, m

m = B*r*q/v
m = (1.1 * 0.011*1.60*10^-19)/(1363.6364)
m = 1.4197*10^-24 kg

Part b:
Velocity, v = 5*10^4 m/s
magnatic field , B = 1.1 * 10^-3 T

Force in magnatic field is given as :
F = q*v*B*Sin(Theta)
F = 1.6*10^-19* 5*10^4* 1.1*10^-3* Sin90
F = 8.8*10^-18 N