A proton and an alpha particle both enter a region of uniform magnetic field B, moving at right angles to the field B. If the radius of circular orbits for both the particles is equal and the kinetic energy acquired by proton is 1 MeV, the energy acquired by the alpha particle will be:

  • Option 1)

    0.5 MeV

  • Option 2)

    1.5 MeV

  • Option 3)

    1 MeV

  • Option 4)

    4 MeV

 

Answers (1)

R=\frac {mv}{qB} = \frac {\sqrt{2mk}}{qB}K_{p}=\frac {q^{2}B^{2}R_{p}^{2}}{2mp},\: K\infty = \frac{q_{\infty}^{2}B^{2}R_{\infty}^{2}}{2m\infty}

K=\frac {q^{2}B^{2}R^{2}}{2m}

\therefore \frac{K\infty}{K_{p}}=\left ( \frac{q\infty}{q_{Io}} \right )^{2} \left ( \frac{mp}{m\infty} \right )\left ( \frac{Rp}{R\infty} \right )^{2}

=>K_{\infty}=K_{p} \left ( \frac{q_{\infty}}{q_{p}} \right )^{2}\left ( \frac{mp}{m\infty} \right )\left ( \frac{R_{\infty}}{R_{p}} \right )^{2}

Kp=1MeV(2)^{2} (\frac{1}{4}) (1)^{2}=1mev

 

 


Option 1)

0.5 MeV

This is incorrect answer

Option 2)

1.5 MeV

This is incorrect answer

Option 3)

1 MeV

This is correct answer

Option 4)

4 MeV

This is incorrect answer

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