Alpha particles (charge = +2e, mass = 6.68 × 10-27 kg) are accelerated in a cyclotron to a final orbit radius of 0.30 m. The magnetic field in the cyclotron is 0.80 T. The period of the circular motion of the alpha particles is closest to: A. 0.25 μs B. 0.16 μs C. 0.49 μs D. 0.40 μs E. 0.33 μs

Option B: T ≈ 0.16 μs

Explanation:

We are given;

Mass; m = 6.68 × 10^(-27) kg

Magnetic field;B = 0.80 T

Charge;q = 2e

Now, e is the charge on an electron and it has a value of 1.6 × 10^(-19) C

So, q = 2 × 1.6 × 10^(-19)

q = 3.2 × 10^(-19) C

The period of the circular motion of the alpha particles moving along a in the presence of the magnetic field is given by;

T = 2πm/qB

Where ;

m, q and B are as stated earlier.

Plugging in the relevant values, we have;

T = (2π × 6.68 × 10^(-27))/(3.2 × 10^(-19) × 0.8)

T = 0.16395 × 10^(-6) s

This can also be written as;

T ≈ 0.16 μs

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