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Bohr's Model of a Hydrogen Atom

Three charged...

Question

Three charged particles a proton, $H e^{+ +}$ and $L i^{+ + +}$ having same kinetic energy enter a region of uniform magnetic field $B_{0}$ perpendicular to it. If $R_{p}, R_{H}$ and $R_{L}$ represent radius of their circular path in field of proton, $H e^{+ +}$ and $L i^{+ + +}$ respectively, then correct relationship between them is

A

R_{p} > R_{H} > R_{L}

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B

R_{p} = R_{H} > R_{L}

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C

R_{p} = R_{H} < R_{L}

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D

R_{p} > R_{H} = R_{L}

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Solution

The correct option is B $R_{p} = R_{H} > R_{L}$
$R = \frac{m v}{q B} = \frac{\sqrt{2 m E}}{q B} \Rightarrow R_{p} = \frac{\sqrt{2 m E}}{e B}$

$R_{H} = \frac{\sqrt{2 \times 4 m E}}{2 e B}$ and $R_{L} = \frac{\sqrt{2 \times 7 m E}}{3 e B}$

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