A cyclotron’s oscillator frequency is 10 MHz. What should be the ope

1.	A cyclotron’s oscillator frequency is 10 MHz. What should be the operating magnetic field for accelerating protons? If the radius of its ‘dees’ is 60 cm, what is the kinetic energy (in MeV) of the proton beam produced by the accelerator. (e =1.60 × 10–19 C, mp = 1.67 × 10–27 kg, 1 MeV = 1.6 × 10–13 J).
Answer» The oscillator frequency should be same as proton’s cyclotron frequency. we have B = 2πmv /q = 6.3 ×1.67 × 10^–27 × 10⁷ / (1.6 × 10^–19) = 0.66 T Final velocity of protons is v = r × 2πv = 0.6 m × 6.3 ×10⁷ = 3.78 × 10⁷ m/s. E = ½ mv² = 1.67 ×10^–27 × 14.3 × 10¹⁴ / (2 × 1.6 × 10^–13) = 7 MeV.

A cyclotron’s oscillator frequency is 10 MHz. What should be the operating magnetic field for accelerating protons? If the radius of its ‘dees’ is 60 cm, what is the kinetic energy (in MeV) of the proton beam produced by the accelerator. (e =1.60 × 10–19 C, mp = 1.67 × 10–27 kg, 1 MeV = 1.6 × 10–13 J).

Answer»

The oscillator frequency should be same as proton’s cyclotron frequency.

we have B = 2πmv /q = 6.3 ×1.67 × 10^–27 × 10⁷ / (1.6 × 10^–19) = 0.66 T

Final velocity of protons is

v = r × 2πv = 0.6 m × 6.3 ×10⁷ = 3.78 × 10⁷ m/s.

E = ½ mv² = 1.67 ×10^–27 × 14.3 × 10¹⁴ / (2 × 1.6 × 10^–13) = 7 MeV.