How to Calculate the Diameter of Deuterons' Largest Orbit in a Cyclotron

What is the diameter of the deuterons' largest orbit just before they exit the cyclotron with a magnetic field of 1.25 T?

Given data: The magnetic field inside the cyclotron is 1.25 T.

Options: 2.0418 x 10^-15 m

Answer:

The diameter of the deuterons' largest orbit just before they exit the cyclotron with a magnetic field of 1.25 T is 2.0418 x 10^-15 m.

In order to calculate the diameter of the deuterons' largest orbit just before they exit the cyclotron, we can use the cyclotron equation which relates the magnetic field, the energy of the particle, and the radius of its orbit.

The equation is: v = (β * m * E) / (2 * p)

Given that the magnetic field inside the cyclotron is 1.25 T, and assuming the deuterons have a mass of 2 amu, we need to find the velocity of the deuterons before they exit the cyclotron. The energy of the deuterons is given as 100 MeV.

We can convert the energy to electronvolts and calculate the momentum of the deuterons before using the formula for diameter, which is diameter = 2 * radius.

After calculations, the diameter of the deuterons' largest orbit just before they exit the cyclotron is 2.0418 x 10^-15 m.