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A cyclotron is operating at a frequency of 
Mass of deuteron is 
and charge on deuteron is 
induction of the neccessary magnetic
Mass of deuteron is and charge on deuteron is induction of the neccessary magnetic field is
- a)0.016 T
- b)0.16 T
- c)16 T
- d)1.6 T
Correct answer is option 'D'. Can you explain this answer?
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To determine the induction of the necessary magnetic field in the cyclotron, we can use the formula for the cyclotron frequency:
f = qB/(2πm)
where f is the frequency, q is the charge on the particle, B is the magnetic field, and m is the mass of the particle.
Given:
Frequency, f = 12 * 10^6 Hz
Charge on deuteron, q = 1.6 * 10^-19 C
Mass of deuteron, m = 3.3 * 10^-27 kg
Let's plug in the values and solve for B.
1. Rearrange the formula to solve for B:
B = (2πmf)/q
2. Substitute the given values:
B = (2π * 3.3 * 10^-27 kg * 12 * 10^6 Hz)/(1.6 * 10^-19 C)
3. Simplify the expression:
B = (2π * 3.3 * 12)/(1.6) * 10^-27 * 10^6 / 10^-19
B = (2π * 39.6)/(1.6) * 10^-27 * 10^6 / 10^-19
B = (2π * 39.6)/(1.6) * 10^(-27+6+19)
B = (2π * 39.6)/(1.6) * 10^(-2)
B = (2π * 39.6)/(1.6) * 10^(-2)
B = (2π * 39.6)/(1.6) * 10^(2)
B = 2π * 39.6 * 10^(2-1)
B = 2π * 39.6 * 10
B = 2 * 3.14 * 39.6 * 10
B ≈ 2 * 3.14 * 40 * 10
B ≈ 2 * 3.14 * 400
B ≈ 6.28 * 400
B ≈ 2512 T
Therefore, the induction of the necessary magnetic field in the cyclotron is approximately 2512 T.
Since none of the given options match the calculated value, it seems there might be an error in the question or answer choices.
f = qB/(2πm)
where f is the frequency, q is the charge on the particle, B is the magnetic field, and m is the mass of the particle.
Given:
Frequency, f = 12 * 10^6 Hz
Charge on deuteron, q = 1.6 * 10^-19 C
Mass of deuteron, m = 3.3 * 10^-27 kg
Let's plug in the values and solve for B.
1. Rearrange the formula to solve for B:
B = (2πmf)/q
2. Substitute the given values:
B = (2π * 3.3 * 10^-27 kg * 12 * 10^6 Hz)/(1.6 * 10^-19 C)
3. Simplify the expression:
B = (2π * 3.3 * 12)/(1.6) * 10^-27 * 10^6 / 10^-19
B = (2π * 39.6)/(1.6) * 10^-27 * 10^6 / 10^-19
B = (2π * 39.6)/(1.6) * 10^(-27+6+19)
B = (2π * 39.6)/(1.6) * 10^(-2)
B = (2π * 39.6)/(1.6) * 10^(-2)
B = (2π * 39.6)/(1.6) * 10^(2)
B = 2π * 39.6 * 10^(2-1)
B = 2π * 39.6 * 10
B = 2 * 3.14 * 39.6 * 10
B ≈ 2 * 3.14 * 40 * 10
B ≈ 2 * 3.14 * 400
B ≈ 6.28 * 400
B ≈ 2512 T
Therefore, the induction of the necessary magnetic field in the cyclotron is approximately 2512 T.
Since none of the given options match the calculated value, it seems there might be an error in the question or answer choices.
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A cyclotron is operating at a frequency of Mass of deuteron is and charge on deuteron is induction of the neccessary magneticfield is a)0.016 Tb)0.16 Tc)16 Td)1.6 TCorrect answer is option 'D'. Can you explain this answer?
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