An electron,a proton,a deuteron,and an alpha | vedclass

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(C) The radius of a charged particle moving in a magnetic field is given by $r = \frac{mv}{qB}$.Since the speed $v$ and magnetic field $B$ are constan

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$R_d = R_\alpha$

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(C) The radius of a charged particle moving in a magnetic field is given by $r = \frac{mv}{qB}$.Since the speed $v$ and magnetic field $B$ are constant for all particles,we have $r \propto \frac{m}{q}$,or $r \propto \frac{1}{(q/m)}$.For the given particles:$1$. Electron $(e^-)$: charge $q$,mass $m_e$.$2$. Proton $(p^+)$: charge $q$,mass $m_p \approx 1836 m_e$.$3$. Deuteron $(d)$: charge $q$,mass $m_d \approx 2 m_p$.$4$. Alpha particle $(\alpha)$: charge $2q$,mass $m_\alpha \approx 4 m_p$.Comparing the charge-to-mass ratios $(q/m)$:$(q/m)_d = q / (2 m_p) = 0.5 (q/m_p)$$(q/m)_\alpha = 2q / (4 m_p) = 0.5 (q/m_p)$Since $(q/m)_d = (q/m)_\alpha$,it follows that $R_d = R_\alpha$.

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