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The energy of emergent protons in MeV from a cyclotron having radius of its dees 1.8 m and applied magnetic field 0.7T is (mass of proton = 1.67×10−27 kg):
- a)50
- b)60
- c)70
Correct answer is option ''. Can you explain this answer?
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The energy of emergent protons in MeV from a cyclotron having radius o...
= 1.22 x 10-11 j = 76 MeV
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The energy of emergent protons in MeV from a cyclotron having radius o...
× 10^-27 kg, charge of proton = 1.6 × 10^-19 C)
We can use the formula for the cyclotron frequency to find the energy of emergent protons:
f = qB/(2πm)
where f is the frequency, q is the charge of the particle, B is the magnetic field, and m is the mass of the particle.
For a proton, q = 1.6 × 10^-19 C and m = 1.67 × 10^-27 kg. Substituting these values and solving for f, we get:
f = (1.6 × 10^-19 C)(0.7 T)/(2π)(1.67 × 10^-27 kg) = 4.2 × 10^7 Hz
The time period of the cyclotron is given by:
T = 1/f = 1/(4.2 × 10^7 Hz) = 2.4 × 10^-8 s
The radius of the cyclotron is 1.8 m, so the circumference is:
C = 2πr = 2π(1.8 m) = 11.3 m
The speed of the protons in the cyclotron is:
v = C/T = (11.3 m)/(2.4 × 10^-8 s) = 4.71 × 10^8 m/s
The kinetic energy of the protons is:
KE = (1/2)mv^2 = (1/2)(1.67 × 10^-27 kg)(4.71 × 10^8 m/s)^2 = 3.69 MeV
Therefore, the energy of emergent protons in MeV from the cyclotron is 3.69 MeV.
We can use the formula for the cyclotron frequency to find the energy of emergent protons:
f = qB/(2πm)
where f is the frequency, q is the charge of the particle, B is the magnetic field, and m is the mass of the particle.
For a proton, q = 1.6 × 10^-19 C and m = 1.67 × 10^-27 kg. Substituting these values and solving for f, we get:
f = (1.6 × 10^-19 C)(0.7 T)/(2π)(1.67 × 10^-27 kg) = 4.2 × 10^7 Hz
The time period of the cyclotron is given by:
T = 1/f = 1/(4.2 × 10^7 Hz) = 2.4 × 10^-8 s
The radius of the cyclotron is 1.8 m, so the circumference is:
C = 2πr = 2π(1.8 m) = 11.3 m
The speed of the protons in the cyclotron is:
v = C/T = (11.3 m)/(2.4 × 10^-8 s) = 4.71 × 10^8 m/s
The kinetic energy of the protons is:
KE = (1/2)mv^2 = (1/2)(1.67 × 10^-27 kg)(4.71 × 10^8 m/s)^2 = 3.69 MeV
Therefore, the energy of emergent protons in MeV from the cyclotron is 3.69 MeV.
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The energy of emergent protons in MeV from a cyclotron having radius of its dees 1.8 m and applied magnetic field 0.7T is (mass of proton = 1.67×10−27kg):a)50b)60c)70Correct answer is option ''. Can you explain this answer?
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