2 questions, but offering the most points rewarded* 1. If in a cyclotron the pro

Question

2 questions, but offering the most points rewarded*

1. If in a cyclotron the proton (m=1.67x10-27kg, charge=1.6x10-19C) aquires an energy of about 100eV per round trip, and the radius of the orbit is 20cm, then what is the distance in meters(m) the proton travels in acquiring an energy of 2 MeV?

2. Calculate the wavelength associated with 1500 MHz- u-waves? If you were to design a traveling waveguide such that the disks were one-quarter wavelength apart, how far apart would they be for this power accelerator?

Explanation / Answer

total round trip numbers=2*10^6/100=2*10^4
so total distance=2*10^4*(2*pi*radius)=2.5133*10^4 m

Q2. wavelength*frequency=speed

so wavelength=speed/frequency=3*10^8/(1500*10^6)=0.2 m

one quarter of wavelength=(1/4)*0.2=0.05 m=5 cm

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