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  • Proton, Deuteron and alpha particle of the same kinetic energy are moving in circular trajectories in a constant magnetic field. The radii of proton, deuteron and alpha particle are respectively <i

Proton, Deuteron and alpha particle of the same kinetic energy are moving in circular trajectories in a constant magnetic field. The radii of proton, deuteron and alpha particle are respectively r_{p},\; r_{d},\; and\; r_{\alpha } . Which one of the following relations is correct?

Option: 1

r_{\alpha }=r_{p}=r_{d}


Option: 2

r_{\alpha }=r_{p}< r_{d}


Option: 3

r_{\alpha }> r_{d}> r_{p}


Option: 4

r_{\alpha }= r_{d}> r_{p}


Answers (1)

As we discussed in

r=\frac{\sqrt{2mk}}{qB}\:\:\:\:=>r\alpha \frac{\sqrt{m}}{q}

r_{p}:r_{d}:r_{\alpha }= \frac{\sqrt{m_{p}}}{q_{p}}: \frac{\sqrt{m_{d}}}{q_{d}}: \frac{\sqrt{m_{\alpha }}}{q_{\alpha }}=>\frac{\sqrt{m}}{e}:\frac{\sqrt{2m}}{e}:\frac{\sqrt{4m}}{2e}

= 1:\sqrt{2}:1\:=>r_{\alpha }=r_{p}<r_{d}

 

Posted by

Kshitij

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