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In a cyclotron, the orbital radius of protons with energy 300KeV is 16.0cm . You are redesigning the cyclotron to be used instead for alpha particles with energy 300 KeV . An alpha particle has charge q = +2e and mass m =6.64×10-27kg . If the magnetic field isn’t changed, what will be the orbital radius of the alpha particles?

Short Answer

Expert verified

The orbital radius of the alpha particles is 16.0 cm

Step by step solution

01

Definition of Magnetic field

The term magnetic field may be defined as the area around the magnet behave like a magnet.

02

Determine the orbital radius of the alpha particles

The radius formula used R=2mKqB

For protonRP=2mpKeBand for alpha particle Rα=2mαKeB

Divide Rαby Rpget

RαRp=2eB2mαK2eB2mpKRαRp=1mα2mp

The mass of proton is 14time mass of the alpha particle so

RαRp=14mp2mpRp=16.0cmRα=16.0cm

Hence, the orbital radius of the alpha particles is 16.0 cm .

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