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Particles of mass 1.6xx10^(-27) kg and c...

Particles of mass `1.6xx10^(-27)` kg and charge `1.6xx10^(-19)C` are accelerated in a cyclotron of dee radius 40cm. It employs a magnetic field 0.4T. Find the kinetic energy (in MeV) of the particle beam imparted by the accelerator.

Text Solution

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Here mass of charged particle `m=1.6xx10^(-27)kg`, charge `q=1.6xx10^(-19)C`, radius of dee `R=40cm=0.4m` and magnetic field B = 0.4T.
`therefore` Kinetic energy of the particle beam imparted by the cyclotron accelerator
`K_("max")=(B^(2)q^(2)R^(2))/(2m)=((0.4)^(2)xx(1.6xx10^(-19))^(2)xx(0.4)^(2))/(2xx(1.6xx10^(-27)))J`
`=((0.4)^(2)xx(1.6xx10^(-19))^(2)xx(0.4)^(2))/(2xx(1.6xx10^(-27))xx(1.6xx10^(-13)))=128MeV`
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