Question:
A deuteron and an alpha particle having equal kinetic energy enter perpendicular into a magnetic field. Let $r_{d}$ and $r_{\alpha}$ be their respective radii of
circular path. The value of $\frac{r_{d}}{r_{\alpha}}$ is equal to :
Correct Option: , 2
Solution:
$r=\frac{m v}{q B}=\frac{\sqrt{2 m k}}{q B}$
$\frac{\mathrm{r}_{\mathrm{d}}}{\mathrm{r}_{\alpha}}=\sqrt{\frac{\mathrm{m}_{\mathrm{d}}}{\mathrm{m}_{\alpha}} \frac{\mathrm{q}_{\mathrm{\alpha}}}{\mathrm{q}_{\mathrm{d}}}}=\sqrt{\frac{2}{4}}\left(\frac{2}{1}\right)=\sqrt{2}$
Hence option (2).
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