Medical cyclotrons need efficient sources of protons to inject into their center. In one kind of ion source, hydrogen atoms (i.e., protons with one orbiting electron) are fed into a chamber where there is a strong magnetic field. Electrons in this chamber are trapped in tight orbits, which greatly increases the chance that they will collide with a hydrogen atom and ionize it. One such source uses a magnetic field of 70 mT, and the electrons' kinetic energy is 1.4 eV. If the electrons travel in a plane perpendicular to the field, what is the radius of their orbits? Express your answer with the appropriate units.
Step 1: Using given kinetic energy, find speed of electron when it enters into magnetic field:
KE = (1/2)*m*V^2
V = sqrt (2*KE/m)
V = sqrt (2*1.4*1.6*10^-19/(9.1*10^-31)) = 701646.415 m/s
Now Using force balance on electron in magnetic field
Fc = Fm
m*V^2/R = q*V*B
R = radius of path = m*V/(q*B)
Using given values
R = 9.1*10^-31*701646.415/(1.6*10^-19*70*10^-3)
R = 57.0*10^-6 m
Let me know if you've any query.
Medical cyclotrons need efficient sources of protons to inject into their center. In one kind of...
Medical cyclotrons need efficient sources of protons to inject into their center. In one kind of ion source, hydrogen atoms (i.e., protons with one orbiting electron) are fed into a chamber where there is a strong magnetic field. Electrons in this chamber are trapped in tight orbits, which greatly increases the chance that they will collide with a hydrogen atom and ionize it. One such source uses a magnetic field of 90 mT, and the electrons' kinetic energy is 1.6...