1.

A proton, a deuteron ion and an alpha-particle of equal kinetic energy perform circular motion normal to a uniform magnetic field B. If the radii of their paths are r_(p),r_(d)andr_(alpha) respectively then _____ [Here, q_(d)=q_(p),m_(d)=2m_(p)]

Answer»

`r_(alpha)=r_(p)ltr_(d)`
`r_(alpha)=r_(d)gtr_(p)`
`r_(alpha)gtr_(d)gtr_(p)`
`r_(alpha)=r_(d)=r_(p)`

Solution :Centripetal force required electric charge `(mv^(2))/r=qvB`
`thereforev=(QBR)/m""...(1)`
Kinetic ENERGY of electric charge = K = `1/2mv^(2)`
= `1/2m((qBr)/m)^(2)`
`thereforeK=(Q^(2)B^(2)r^(2))/(2m)`
`thereforer^(2)=(2Km)/(q^(2)B^(2))rArrrpropsqrtm/q`
`thereforer_(alpha):r_(p):r_(d)=sqrt4/2:sqrt1/(1)1:sqrt2/1`
= `1:1:sqrt2`
`thereforer_(alpha)=r_(p)ltr_(d)`


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