Question

A cyclotron is used to produce a beam of high-energy deuterons that then collide with a target to produce radioactive isotopes for a medical procedure. Deuterons are nuclei of deuterium, an isotope of hydrogen, consisting of one neutron and one proton, with total mass 3.34×10−27kg. The deuterons exit the cyclotron with a kinetic energy of 4.60 MeV .

1. What is the speed of the deuterons when they exit?

2. If the magnetic field inside the cyclotron is 1.25 T, what is the diameter of the deuterons' largest orbit, just before they exit?

3. If the beam current is 450 μA how many deuterons strike the target each second?

Answer 1

To solve this problem you have to know about Kinetic energy and Magnetic field

Step 1.

Definition:

Kinetic energy: Kinetic energy is an expression of the fact that a moving object can do work on whatever strikes ; quantifies the amount of work that the object might take as a result of their movement.

Magnetic field: A magnetic field is a force field created as a result of the motion of electric charges.

Step 2.

1.-

2.-

The only force acting on the system is the force produced by the magnetic field , and the centripeta force , then equate the equation

3.-

The current is: , where the current is the charge per time unit

then a second charge amount is

Now for calculate how many deuterons strike is target each second the charge we divide the load between the load deutrons

If you have any question please let me know in the comments