9.2 Problems 499
9.78 In a betatron of diameter 72 in operating at 50 c/s the maximum magnetic field
is 1.2Wb/m^2. Calculate
(a) the number of revolutions made each quarter cycle
(b) the maximum energy of the electrons
(c) the average energy gained per revolution
[University of New Castle 1965]
9.2.12 Cyclotron.........................................
9.79 A cyclotron is designed to accelerate protons to an energy of 6 MeV. Deduce
the expression for the kinetic energy in terms of radius, magnetic field etc and
calculate the maximum radius attained.
[University of Bristol 1967]
9.80 If the acceleration potential (peak voltage, 50,000) has a frequency of 1. 2 ×
107 c/s, find the field strength for cyclotron resonance when deuterons and
alpha particles, respectively are accelerated. For how long are the parti-
cles accelerated if the radius of orbit at ejection is 30.0 cm? Deuteron rest
mass= 2 .01 amu.α-particle rest mass= 4 .00 amu
[University of New Castle 1965]
9.81 The original (uniform magnetic field) type of fixed frequency cyclotron was
limited in energy because of the relativistic increase of mass of the accelerated
particle with energy. What percentage increment to the magnetic flux density
at extreme radius would be necessary to preserve the resonance condition for
protons of energy 20 MeV?
[University of Durham 1972]
9.82 A cyclotron is powered by a 50,000 V, 5 Mc/s radio frequency source. If its
diameter is 1.524 m. what magnetic field satisfies the resonance conditions for
(a) protons (b) deuterons (c) alpha-particles? Also what energies will these
particles attain?
[University of Durham 1961]
9.83 In a synchrocyclotron, the magnetic flux density decreases from 15,000 G at
the centre of the magnet to 14,300 G at the limiting radius of 206 cm. Calculate
the range of frequency modulation required for deuteron acceleration and the
maximum kinetic energy of the deuteron. (The rest mass of the deuteron is
3. 34 × 10 −^24 g)
[University of London 1959]
9.84 Calculate the magnetic field,Band the Dee radius of a cyclotron which will
accelerate protons to a maximum energy of 5 MeV if a radio frequency of
8 MHz is available.
9.85 When a cyclotron shifts from deuterons to alpha particles it is necessary to
drop the magnetic field slightly. If the atomic masses of^2 H and^4 He are
2.014102 amu and 4.002603 amu, what is the percentage decrease in field
strength that is required?
[Osmania University]