A cyclotron is used to accelerate neon nuclei (charge 10e^+, mass 20m_p) from re

Question

A cyclotron is used to accelerate neon nuclei (charge 10e^+, mass 20m_p) from rest up to an energy of 600 keV. The magnetic field is 500 G. What is the particle's final speed? What is the minimum radius of the magnet in order to accommodate a 600 keV kinetic energy? What is the cyclotron frequency (express answer in kHz)? If the alternating potential applied to the dees is 3 kV, how many revolutions are necessary to accelerate a nucleus up to that energy? 355 How long will it take for the nucleus to reach that kinetic energy (express answer in ps)? If it is sent through a velocity selector, what is the necessary electric field strength E_s if the magnetic field is B_s = 1 T? Draw a diagram of this entire experiment, clearly labeling all relevant parts both within the cyclotron and in the velocity selector.

Explanation / Answer

a) Gain in KE = 600 keV

              = 600 x 10^3 x 1.6 x 10^-19 J

            = 9.6 x 10^-14 J

20 x 1.673 x 10^-27 x v^2 /2 = 9.6 x 10^-14

v = 2.4 x 10^6 m/s

b) magnetic force = m v^2 / r

q v B = m v^2 / r

r = m v / q B = (20 x 1.673 x 10^-27) ( 2.4 x 10^6) / (10 x 1.6 x 10^-19)(500 x 10^-4)

= 0.98 m

c) f = v / 2pir = (2.4 x 10^6) / (2 x pi x 0.98)

      = 3.9 x 10^5 Hz

d) revolutions = 600/3 =200

e) time = 200 / f = 200 / 3.9x10^5 = 5.13 x 10^-4 sec

f) E = v B

E = 2.4 x 10^6 x 1 = 2.4 x 10^6 N/C

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