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Cyclotrons are widely used in nuclear medicine for producing short-lived radioactive isotopes. These cyclotrons typically accelerate H-(the hydride ion, which has one proton and two electrons) to an energy of 5MeVto20MeV.This ion has a mass very close to that of a proton because the electron mass is negligible about 12000of the proton’s mass. A typical magnetic field in such cyclotrons is 1.9T..(a) What is the speed of a 5.0-MeVH-? (b) If the H-has energy 5.0MeVandB=1.9T what is the radius of this ion’s circulator orbit?

Short Answer

Expert verified

(a) The speed of a 5.0_MeVH-is3.1×107m/s

(b) The radius of this ion’s circulator orbit is 0.17 m

Step by step solution

01

Definition of isotopes

The term isotopes may be defined as the allotropes having same atomic number but different mass number.

02

Determine the speed of a 5.0-MeV H-

AccordingtolawofconservationofenergyKi+Ui=Kf+Uf,Ki=0soKf=Uf-UiputgivenvalueKf=5.0MeVNowKf=5.0×1.6×10-19×106JFurther12mv2=5.0×1.6×10-19×106Jv=2m×1.6×10-19×106Jv=3.1×107m/sHence,thespeedofa5.0-MeVH-is3.1×107m/s

03

Determine the radius of this ion’s circulator orbit

FortheradiususingrelationR=1.67×10-27kg3.1×107m/s1.6×10-191.9TR=0.17mHence,theradiusofthisionscirculatororbitis0.17m

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