Magnetic Effects & Magnetism

JEE Main level, single correct, medium

165 of 276

Question 165 of 276

An electron, a proton and an alpha particle having the same kinetic energy are moving in circular orbits of radii re,rp,rα{r}_{e},{r}_{p},{r}_{\alpha } respectively in a uniform magnetic field B. The relation between re,rp,rα{r}_{e},{r}_{p},{r}_{\alpha } is:

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Answer: (C) re<rp=rα{r}_{e}\lt {r}_{p}={r}_{\alpha }

r=mVqB=2mKqBr=\dfrac{mV}{qB}=\dfrac{\sqrt{2mK}}{qB}⇒r∝mq\Rightarrow r\propto \dfrac{\sqrt{m}}{q}. For electron, re=kmee{r}_{e}=k\dfrac{\sqrt{{m}_{e}}}{e} Where, me{m}_{e} is the mass of an electron. m=m=the mass of a proton. For alpha particles, rα=k4m2e=kme{r}_{\alpha }=k\dfrac{\sqrt{4m}}{2e}=k\dfrac{\sqrt{m}}{e}, q=q=charge on proton. For proton, rp=kme{r}_{p}=k\dfrac{\sqrt{m}}{e}, so, re<rp=rα{r}_{e}\lt {r}_{p}={r}_{\alpha }.

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