Please show ALL work with correct units Thank you 18 Estimat

Please show ALL work with correct units. Thank you.

18. Estimate the total path length traveled by a deuteron (a heavy hydrogen nucleus consisting of a proton and a neutron) in a cyclotron of radius 53 cm and operating frequency 12 Mhz during the entire acceleration process. The accelerating potential between the dees is 80 kV.

Solution

the potential between the dees, V = 80*10³ V

Charge of the deuteron, e =1.6*10^-19 C

The magnetic field is

      B = ( 2mf) / e

Here m = 3.344x10^-27 kg and f = 12*10⁶Hz

then,

        B =  (2(3.344x10^-27 kg)(12*10⁶Hz)) /(1.6*10^-19C) = 1.575 T

Hence the total path length is,

    x = (2/B)sqrt[2mV/e] = 0.899 m = 0.9 m