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  • A proton, a deuteron and an C-particle with same kinetic energy enter into a uniform magnetic field at right angle to magnetic field. The ratio of the radii of their respective circular paths is :<

A proton, a deuteron and an C-particle with same kinetic energy enter into a uniform magnetic field at right angle to magnetic field. The ratio of the radii of their respective circular paths is :

Option: 1

1:\sqrt{2}:\sqrt{2}


Option: 2

1:1:\sqrt{2}


Option: 3

\sqrt{2}:1:1


Option: 4

1:\sqrt{2}:1


Answers (1)

It is given that,
\mathrm{\bar{V} \perp \bar{B}} (for all particles)

\begin{array}{ll} K E_{\alpha}=K E_{D}=K E_{p}\\ m_{\alpha}=4 a m u ;\ q_{\alpha}=2 e \\ m_{D}=2 a m u ;\ q_{D}=1 e \\ m_{p}=1 a m p ; \ q_{p}=1 e \end{array}

We know that,
\mathrm{ \begin{aligned} \gamma=\frac{m v}{q_{B}} &=\frac{\sqrt{2 m k E}}{q B} \\ \gamma_{p}: \gamma_{D}: \gamma_{\alpha} &=\frac{\sqrt{m_{p}}}{q_{p}}: \frac{\sqrt{m_{D}}}{q_{D}}: \frac{\sqrt{m_{\alpha}}}{q_{\alpha}} \\ &=1: \sqrt{2}: 1 \end{aligned} }
The correct option is (4)

Posted by

Ramraj Saini

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