An electron and a proton enter region of uniform magnetic field in a direction at right angles to the field with the same kinetic energy. They describe circular paths of radius ${r_e}$ and ${r_p}$ respectively. Then
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(b) $r = \frac{{\sqrt {2mK} }}{{qB}}i.e.\;\;r \propto \frac{{\sqrt m }}{q}$
Here kinetic energy $K$ and $B$ are same.
Here kinetic energy $K$ and $B$ are same.
$\therefore \;\frac{{{r_e}}}{{{r_p}}} = \sqrt {\frac{{{m_e}}}{{{m_p}}}} \times \frac{{{q_p}}}{{{q_e}}} \Rightarrow \frac{{{r_e}}}{{{r_p}}} = \sqrt {\frac{{{m_e}}}{{{m_p}}}} \;\;(\because \;{q_e} = {q_p})$
Since $m_e < m_p$, therefore $ r_e < r_p$
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