Magnetic Effects & Magnetism

JEE Main level, single correct, medium

159 of 276

Question 159 of 276

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 rp,re{r}_{p},{r}_{e} and rHe{r}_{He} be their respective radii, then,

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Answer: (B) re<rp=rHe{r}_{e}\lt {r}_{p}={r}_{He}

We know, r=mvqB(∵K.E.=12mv2)r=\dfrac{mv}{qB}\left(∵\text{K.E.=}\dfrac{1}{2}m{v}^{2}\right)
=2mK.E.qB=\dfrac{\sqrt{2mK.E.}}{qB}
∴∴ K.E. is same for all particle and magnetic field B is also some.
r∝mqr\propto \dfrac{\sqrt{m}}{q}
For proton: rp∝mpe{r}_{p}\propto \dfrac{\sqrt{{m}_{p}}}{e}
For electron: re∝mee{r}_{e}\propto \dfrac{\sqrt{{m}_{e}}}{e}
For Helium nuclei: rHe∝4mp2e=mpe{r}_{He}\propto \dfrac{\sqrt{4{m}_{p}}}{2e}=\dfrac{\sqrt{{m}_{p}}}{e}

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