Two isotoprs of uranium U235(3.9x10^-25 kg) , U238(3.95x10^-25kg) into spectrometer (1.05x10^5 m/s). Each isotope is singly ionized and B field(0.75T). What is the distance between the two isotopes?

1 Answer
Apr 2, 2016

Answer:

#0.875cm#

Explanation:

Given that two isotopes of Uranium #"U"235(3.9xx10^-25 kg) and "U"238(3.95xx10^-25kg)# into spectrometer.
Velocity of each singly ionized atom is #1.05xx10^5 m//s#
Force #vecF #on a charged particle due to magnetic field #=q(vecvxxvecB)#

Since the magnetic field is perpendicular to the direction of motion in a spectrometer
#|vecF|=q.|vecv|.|vecB|#, singly ionized atom has charge #1.60xx 10^-19C#

This magnetic force produces circular motion of the ion.
Centripetal force #(m.v^2)/r=|vecF|#, where #r# is the radius of circle in which ion moves.
#(m.v^2)/r=q.|vecv|.|vecB|#, Solving for #r#
#r=(m.|vecv|)/(q.|vecB|)#

#r=(mxx1.05xx10^5)/(1.60xx 10^-19xx0.75)#

#r=mxx8.75xx10^23#

  1. For #"U"235#:
    #r_235=3.9xx10^-25xx8.75xx10^23#
    #=0.34125m#
  2. For #"U"238#:
    #r_238=3.95xx10^-25xx8.75xx10^23#
    #=0.345625m#

Distance between the two isotopes is equal to difference between the two diameters

buphy.bu.edu
#=2xx(0.345625-0.34125)=0.00875m#
#=0.875cm#