In order to make a nuclear weapon out of uranium, you need a certain amount of \

Question

In order to make a nuclear weapon out of uranium, you need a certain amount of ''good'' uranium. Uranium is more abundant as Uranium 235, but Uranium 238 is considered ''good'' for fission. The numbers 235 and 238 refers to how many neutrons are present in each atom of Uranium. In order to separate 235 from 238, a cyclotron is used. The mass of a Uranium 238 ion is 3.983x10^-25 kg. Uranium is ionized (a single electron is removed from the Uranium atoms) and these ionized atoms are accelerated with an electric potential of V = 120 Volts. After being accelerated, they are fired into a chamber with a magnetic field of B = 1.5 T. There is a target plate positioned right next to where the ions enter the chamber. At what position do the 235 ions hit the plate, and what position do the 238 ions hit the plate?

Explanation / Answer

gain in KE = Workdone on uranium oin

0.5*m*v^2 = q*V

v = sqrt(2*q*V/m)

m*v^2/r = q*v*B

r = m*v/(B*q)

= m*sqrt(2*q*V/m)/(B*q)

= sqrt(2*V*m/q)/(B)

= sqrt(2*120*3.983*10^-25/1.6*10^-19)/(1.5)

= 0.0163 m or 1.63 cm

so U_238 toches the plate at 2*0.0163 = 0.0326 m <<<<<------Answer

u_235 toches the plate at 2*0.0163*sqrt(235/238) = 0.0324 m <<<<<------Answer

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