Question

A proton, a deutron and an α- particle having the same kinetic energy are moving in circular trajectories in

a constant magnetic field. If rp, rd and rα denote respectively the radii of the trajectories of these particles,

then

(a) rα ˃ rd ˃ rp (b) rα= rp˂ rd `` (c) rα= rd ˃ rd (d) rα= rd = rd​

Answer 1

$\huge{\underline{\tt{\red{Answer-}}}}$

(b) rα= rp˂ rd

$\huge{\underline{\tt{\blue{Explanation-}}}}$

The centreipetal force is provided by the magnetic force

$\dfrac{(mv^2)}{r}=qvB \implies \dfrac{(mv)}{r} =qB$

$\implies r=\dfrac{(mv)}{(qB)} =\dfrac{p}{(qB)} [\therefore p=mv]$

$But `KE=\dfrac{(p^2)}{(2m)} \implies p= \sqrt{2mKE}$

Here, KE and B are same for the three particles

$\therefore R \propto \dfrac{(\sqrt m)}{q}$

$\therefore r_p:r_d:r_\alpha=\dfrac{(\sqrt1)}{1}:\dfrac{(\sqrt2)}{1}:\dfrac{(\sqrt4)}{1}=1:\sqrt2:1$

$\implies r_\alpha=r_p < \ r_d$

Mark brainliest Plz_____ :)