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  • A proton and con -partide move perpendicular to a uniform maguetei field. The mass

A proton and con \alpha-partide move perpendicular to a uniform maguetei field. The mass of an \alpha-particle is four times that of a proton and its charge is twice that of a proton. Find the ratio of radii of the Circular path followed by them if both are accelerated through the same potential differences:

Option: 1

1:2


Option: 2

2:1


Option: 3

1: \sqrt{2}


Option: 4

\sqrt{2}: 1


Answers (1)

best_answer

\begin{aligned} & K=q V \\ \end{aligned}

\begin{aligned} & r=\frac{1}{q B} \cdot \sqrt{2 m q v}=\frac{1}{B} \sqrt{\frac{2 m v}{q}} \\ \end{aligned}

So, \begin{aligned} \frac{r_p}{r_\alpha}=\frac{1 / B \sqrt{2 m_p v} / q_p}{\frac{1}{B} \sqrt{\frac{2 m_\alpha v}{q_\alpha}}} \\ \end{aligned}

            \begin{aligned} &=\sqrt{\frac{m_p}{m_\alpha} \cdot \frac{q_\alpha}{q_p}}=\sqrt{\frac{1}{4} \times 2}=1: \sqrt{2} \end{aligned}

 

 

 

Posted by

Rishabh

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