A deuteron has the same charge as a proton but approximately twice the proton mass. Suppose deuterons are being accelerated in a cyclotron in an orbit of radius 75 cm at a frequency of 8.0 MHz. What magnetic field magnitude is needed? (e = 1.60 × 10^-19 C, ^mproton = 1.67 × 10^-27 kg) A) 0.011 T B) 0.11 T C) 1.1 T D) 11 T E) 110 T

Question

Quizplus · Accepted Answer

The cyclotron equation relates the frequency of rotation to the magnetic field and the radius of rotation:
f = (qB)/(2πm)

where f is the frequency, q is the charge, B is the magnetic field, and m is the mass.

For a deuteron, q = e and m = 2 m_proton. Substituting these values and the given frequency and radius, we have:

8.0 × 10^6 Hz = (1.60 × 10^-19 C)(B)/(2π)(2)(1.67 × 10^-27 kg)(0.75 m)

Solving for B gives:

B ≈ 1.1 T

Therefore, the correct answer is C.

A Deuteron Has the Same Charge as a Proton but Approximately