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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?
Verified Answer
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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Most Upvoted Answer
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.
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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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