Question

Chlorine has two stable isotopes, 35Cl and 37Cl. Chlorine gas which consists of singly ionized ions is to be separated into its isotopic components using a mass spectrometer. The magnetic field strength in the spectrometer is 1.2 T. What is the minimum value of the potential difference through which these ions must be accelerated so that the separation between them, after they complete their semicircular path, is 1.6 cm?

........................MV

Answer 1

let,

d=pi*r=`1.6cm

B=1.2 T

here,

by using force euqation,

m*v^2/r=q*v*B ---(1)

and

by using energy equation,

1/2*m*v^2=q*V --(2)

from (1) and (2)

r=sqrt(2m*V/q*B^2)---(3)

for 35Cl isotope

r1=sqrt(2*m1*V/q*B^2)

and

for 37Cl isotope

r2=sqrt(2*m2*V/q*B^2)

==>

r2-r1=sqrt(2*m2*V/q*B^2) - sqrt(2*m1*V/q*B^2)

but, r2-r2=d/2

d/2=sqrt(2*m2*V/q*B^2) - sqrt(2*m1*V/q*B^2)

d/2=1/B*sqrt(2*V/q)*(sqrt(m2)-sqrt(m1))

(d/2)^2=1/B^2*(2*V/q)*(sqrt(m2)-sqrt(m1))^2

((1.6*10^-2)/2)^2=1/(1.2)^2*2*V/(1.6*10^-19)*(sqrt(37)-sqrt(35))^2*1.66*10^-27

===>V=1.6*10^5 V

or V=0.16*10^6 V

potential difference, dV=0.16 MV