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a. What is the kinetic energy of the protons when they are ejected from the cyclotron? KE at ejection = b. What is this energy in MeV? KE at ejection in MeV = MeV 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 it pass through a magnetic field and confining the protons to a circular path before the next increment in energy. Potential difference = MV d. What is the period of the voltage source used to accelerate the protons? Hint: For maximum energy transfer from the external voltage source to the proton, the period of the oscillating voltage should coincide with the period of oscillation of the proton. Period of the voltage source = S

a. What is the kinetic energy of the protons when they are ejected from the cyclotron? KE at ejection = b. What is this energy in MeV? KE at ejection in MeV = MeV 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 it pass through a magnetic field and confining the protons to a circular path before the next increment in energy. Potential difference = MV d. What is the period of the voltage source used to accelerate the protons? Hint: For maximum energy transfer from the external voltage source to the proton, the period of the oscillating voltage should coincide with the period of oscillation of the proton. Period of the voltage source = S

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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 1.6-10-1⁹ C. Dee O O/O O O OI I O 10 O Ion source O O O O O O Electric oscillator O Deflector plate Target Electric field region where kinetic energy is gained Proton beam
Transcribed Image Text: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 1.6-10-1⁹ C. Dee O O/O O O OI I O 10 O Ion source O O O O O O Electric oscillator O Deflector plate Target Electric field region where kinetic energy is gained Proton beam
a. What is the kinetic energy of the protons when they are ejected from the cyclotron? KE at ejection = J b. What is this energy in MeV? KE at ejection in MeV = MeV 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 it pass through a magnetic field and confining the protons to a circular path before the next increment in energy. Potential difference = MV d. What is the period of the voltage source used to accelerate the protons? Hint: For maximum energy transfer from the external voltage source to the proton, the period of the oscillating voltage should coincide with the period of oscillation of the proton. Period of the voltage source = ✔S
Transcribed Image Text:a. What is the kinetic energy of the protons when they are ejected from the cyclotron? KE at ejection = J b. What is this energy in MeV? KE at ejection in MeV = MeV 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 it pass through a magnetic field and confining the protons to a circular path before the next increment in energy. Potential difference = MV d. What is the period of the voltage source used to accelerate the protons? Hint: For maximum energy transfer from the external voltage source to the proton, the period of the oscillating voltage should coincide with the period of oscillation of the proton. Period of the voltage source = ✔S
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a. What is the kinetic energy of the protons when they are ejected from the cyclotron? KE at ejection = 1.92×10 VI -12 b. What is this energy in MeV? KE at ejection in MeV = 11.98 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 it pass through a magnetic field and confining the protons to a circular path before the next increment in energy. Potential difference = 5.99 MV d. What is the period of the voltage source used to accelerate the protons? Hint: For maximum energy transfer from the external voltage source to the proton, the period of the oscillating voltage should coincide with the period of oscillation of the proton. Period of the voltage source = No, that's only partially correct. MeV X 5.25 X 10 -8 S
Transcribed Image Text:a. What is the kinetic energy of the protons when they are ejected from the cyclotron? KE at ejection = 1.92×10 VI -12 b. What is this energy in MeV? KE at ejection in MeV = 11.98 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 it pass through a magnetic field and confining the protons to a circular path before the next increment in energy. Potential difference = 5.99 MV d. What is the period of the voltage source used to accelerate the protons? Hint: For maximum energy transfer from the external voltage source to the proton, the period of the oscillating voltage should coincide with the period of oscillation of the proton. Period of the voltage source = No, that's only partially correct. MeV X 5.25 X 10 -8 S
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