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A proton, an electron, and a Helium nucl...

A proton, an electron, and a Helium nucleus, have the same Kinetic 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

A

`r_e gtr_p = r_("He")`

B

`r_e gt r_p gt r_("He")`

C

`r_e ltr_p lt r_("He")`

D

`r_e ltr_p = r_("He")`

Text Solution

Verified by Experts

The correct Answer is:
C
Radius of circle is given by
`r=(mv)/(qB) = p/(qB) = (sqrt(2mk))/(qB)=(sqrt(2m))/(qB)sqrtk`
Where K is kinetic energy
For proton `:r_p=(sqrt2m_p)/(eB)sqrtK`
For electron: `,r_e=(sqrt2m_e)/(eB)sqrtK`
For `He^(+) " " : r_("He")=(sqrt(2xx4m_p))/(eB)sqrtK=(2sqrt2m_p)/(eB)sqrtK`
Clearly `r_("He") gt r_p gtr_e`
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