Question

What is the cyclotron frequency of a proton in a magnetic field with a magnitude of 5.20 T?

A) 2.68 × 10^8 Hz
B) 4.78 × 10^8 Hz
C) 8.92 × 10^8 Hz
D) 6.15 × 10^8 Hz

Answer 1

Using the formula for cyclotron frequency, none of the provided options matches the correctly calculated value of A. 2.48 x 10^8 Hz for a proton in a 5.20 T magnetic field.

Step-by-step explanation:

To determine the cyclotron frequency of a proton in a magnetic field, the formula f = (q*B)/(2*π*m) is used, where q is the charge of the proton (1.602 x 10-19 C), B is the magnetic field strength (5.20 T), and m is the mass of the proton (1.672 x 10-27 kg). Plugging these values into the formula gives us:

f = (1.602 x 10-19 C * 5.20 T) / (2 *π* 1.672 x 10-27 kg) = 2.48 x 108 Hz

However, none of the provided options match this value exactly. It's possible there may be a typo or miscalculation. Based on the correct calculation, neither of the options A) 2.68 × 108 Hz, B) 4.78 × 108 Hz, C) 8.92 × 108 Hz, nor D) 6.15 × 108 Hz is correct.