A cyclotron designed to accelerate protons of mass 1.673 x 10^-27 kg to an energy of 5.5 MeV has a diameter of 9m. The charge on a proton is 1.602 x 10^-19 C. What magnetic field must be used?
I think the formula r = mv/qB should be used but i don't know how to convert 5.5 MeV to velocity (m/s) can someone tell me if I'm on the right track? and how to convert MeV to velocity? thanks a bunch!
Change the energy to joules, then set that Kenergy equal to 1/2 mv^2 to get velocity.
thannnnnksss!
You're on the right track! To convert the energy from MeV to velocity, you can use the equation for kinetic energy: Kenergy = 1/2 mv^2, where Kenergy is the energy in joules, m is the mass in kilograms, and v is the velocity in meters per second.
In this case, we need to convert the energy from 5.5 MeV to joules, and then solve for the velocity. To convert MeV to joules, we can use the conversion factor 1 MeV = 1.602 x 10^-13 joules.
So, first, multiply 5.5 MeV by 1.602 x 10^-13 joules/MeV to convert from MeV to joules:
(5.5 MeV) * (1.602 x 10^-13 joules/MeV) = 8.807 x 10^-13 joules.
Now we have the energy in joules. Set this energy equal to 1/2 mv^2 and solve for v:
8.807 x 10^-13 joules = (1/2) * (1.673 x 10^-27 kg) * v^2.
To solve for v, divide both sides of the equation by (1/2) * (1.673 x 10^-27 kg):
v^2 = (8.807 x 10^-13 joules) / [(1/2) * (1.673 x 10^-27 kg)].
Finally, take the square root of both sides to find the velocity v:
v = sqrt[(8.807 x 10^-13 joules) / [(1/2) * (1.673 x 10^-27 kg)]].
Now that you have the velocity, you can use the formula r = mv/qB to solve for the magnetic field (B).