A proton, an electron, and a Helium nucleus, have the same energy.They are in circular orbits in a plane due to magnetic field perpendicular to the plane. Let `r_p,r_e` and `r_(He)` be their respective radii, then,

Options

A. `r_(e)gtr_(p)gtr_(He)`
B. `r_(e)ltr_(p)lt4_(He)`
C. `r_(e)gtr_(p)=r_(He)`
D. `r_(e)ltr_(p)=r_(He)`

Answer

D

Explanation

`r=(mv)/(qB):.r prop (sqrt(m))/q`[ K.E is ome for all particles]
`M_(H_(e)^(2+))=4m_(p), q_(H_(e)^(4))+2q_(p)`
`m_(p)gtm_(e)`
`r_(p)=k(sqrt(m_(p)))/(q_(p)), k=sqrt((2(K.E.))/B), r_(e)=(ksqrt(m_(e)))/(q_(e))`
`r_(Ae^(+4))=(ksqrt(4xxm_(p)))/(2q_(p))=ksqrt((m_(p))/(q_(p))):.r_(e)ltr_(p)=r_(He)`