The magnetic field in a cyclotron is 1.25 T, and the maximum orbital radius of the circulating protons is 0.40 m. (a) What is the kinetic energy of the protons when they are ejected from the cyclotron? (b) What Is this energy in MeV? (c) Through what potential difference would a proton have to be accelerated to acquire this kinetic energy? (d) What is the period of tire voltage source used to accelerate the piotons? (e) Repeat tire calculations for alpha-particles.
The magnetic field in a cyclotron is 1.25 T, and the maximum orbital radius of the circulating protons is 0.40 m. (a) What is the kinetic energy of the protons when they are ejected from the cyclotron? (b) What Is this energy in MeV? (c) Through what potential difference would a proton have to be accelerated to acquire this kinetic energy? (d) What is the period of tire voltage source used to accelerate the piotons? (e) Repeat tire calculations for alpha-particles.
The magnetic field in a cyclotron is 1.25 T, and the maximum orbital radius of the circulating protons is 0.40 m. (a) What is the kinetic energy of the protons when they are ejected from the cyclotron? (b) What Is this energy in MeV? (c) Through what potential difference would a proton have to be accelerated to acquire this kinetic energy? (d) What is the period of tire voltage source used to accelerate the piotons? (e) Repeat tire calculations for alpha-particles.
When a beam of ions each carrying a charge of 3.2 × 10-19 C and of mass 3.3 × 10-27 kg are accelerated through a PD of 2.0kV to enter an evacuated region in a direction at right-angles to a uniform magnetic field. The beam is observed to be deflected into a circular path of radius 9.4cm.
Draw a diagram showing the path taken by the beam in the field. Indicate clearly the direction of the magnetic field you consider.
Explain how you arrived at your diagram.
Explain why the path is circular.
What would have been the shape of the ions' path in the same field if they had entered the field with a uniform deceleration and in the same direction as before? Explain your answer.
The accleration of protons in a cyclotron is shown in the figure below.
The magnetic field in a cyclotron is 1.25 T, and the maximum orbital radius of the circulating protons
is 0.4 m. The mass of a proton is 1.67-10-27 kg and the charge on a proton is 1.6-10-1⁹9 C.
Dee
O
b. What is this energy in MeV?
KE at ejection in MeV =
O
OIOIO
1
1
O
1
10
O
Ion source
O
O
O
O
Electric oscillator
MeV
MV
O
O
1
Electric field region where
kinetic energy is gained
Deflector plate
Target
a. What is the kinetic energy of the protons when they are ejected from the cyclotron?
KE at ejection =
S
Proton beam
c. Through what total potential difference (potential difference between the gaps and number of trips
through the gaps) would a proton have to be accelerated to acquire this kinetic energy?
Think about the magnitude of potential you have calculated. While designing the cyclotron, gap
potential can be made much smaller than this magnitude by making the proton pass through the gap
several times by making…
What value of B should be used in a velocity selector to separate out 2.0-keV protons if E is fixed at 80 kV/m?
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