What Causes Frequency Discrepancies in Particle Accelerator Calculations?

[Amith2006]

I need help. It’s urgent!
# Assume that in the 70 million electron volt (MeV) betatron, the radius of the stable electron orbit is 28 cm. Calculate the frequency of the applied electric field.
I have found the angular velocity of the electron (w) = 1.07 x 10^9
I assumed that the frequency of the electron= frequency of applied electric field
From that I found the frequency(f) of the
w = 2(pi)f
f = 1.7 x 10^8 Hz
But the answer given in my book is 1.7 x 10^6 Hz. Is it a typographic error?

# A linear accelerator for the acceleration of protons to 45.3 MeV is designed so that between any pair of accelerating gaps, the protons spend one complete radio frequency cycle inside a drift tube. The frequency of the radio frequency oscillator is 200 MHz. If the frequency of the accelerating potential is 1.49 x 10^6 volts, what is the total length of the linear accelerator?
I have found the length of the drift tubes individually. By adding the length of all the drift tubes, the length of the linear accelerator can be found out. But that is a time taking process. Is there is better way to find the length of the linear accelerator? I asked my lecturer, he also doesn’t know. Please reply fast because I have my exam tomorrow.

 

[Andrew Mason]

I need help. It’s urgent!
# Assume that in the 70 million electron volt (MeV) betatron, the radius of the stable electron orbit is 28 cm. Calculate the frequency of the applied electric field.
I have found the angular velocity of the electron (w) = 1.07 x 10^9
I assumed that the frequency of the electron= frequency of applied electric field
From that I found the frequency(f) of the
w = 2(pi)f
f = 1.7 x 10^8 Hz
But the answer given in my book is 1.7 x 10^6 Hz. Is it a typographic error?

You have to take into account the relativistic speed here. What did you determine the $\gamma$ to be?

AM