1939 Nobel Prize in Physics is awarded to Ernest O. Lawrence for his efforts in

Question

1939 Nobel Prize in Physics is awarded to Ernest O. Lawrence for his efforts in the development of the cyclotron device. The first cyclotron he built in 1932 had 2R 69 cm diameter "dees" and was using a huge electromagnet he obtained from some company for producing a uniform B1.6 T magnetic field. He accelerated deuterons and protons to very high energies by using this device. (a) Suppose that the cyclotron is adjusted to accelerate the protons. Find the speed of the protons when they come out of the cyclotron. (Mass of proton: mp 1.67 x 10-2 kg.) (b) Find the final kinetic energy of the protons in eV units. (Note: 1 MeV-10 eV) Compare this to the proton energy of 6.5 TeV achievable in the Large Hadron Collider at CERN. (c) An alternating emf has to be applied to the dees to be able to accelerate the protons. Find the angular frequency, w, and the frequency, f, of the alternating emf that should be used.

Explanation / Answer

given

B = 1.6 T

R = 69/2 = 34.5 cm = 0.345 m

m = 1.67*10^-27 kg

a) we know, R = m*v/(B*q)

==> v = B*q*R/m

= 1.6*1.6*10^-19*0.345/(1.67*10^-27)

= 5.29*10^7 m/s

b) KE = (1/2)*m*v^2

= (1/2)*1.67*10^-27*(5.29*10^7)^2

= 2.337*10^-12 J

= 2.337*10^-12/(1.6*10^-19) eV

= 14.6 MeV or 14.6*10^6 eV

KE/KE_CERN = 14.6*10^6/(6.5*10^9)

= 0.00225

c) w = B*q/m

= 1.6*1.6*10^-19/(1.67*10^-27)

= 1.53*10^8 rad/s

f = w/(2*pi)

= 1.53*10^8/(2*pi)

= 2.44*10^7 Hz

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