An α-particle (mass 4 amu ) and a singly charged sulfur ion (mass 32 amu ) are initially at rest. They are accelerated through a potential V and then allowed to pass into a region of uniform magnetic field which is normal to the velocities of the particles. Within this region, the α-particle and the sulfur ion move in circular orbits of radii rα and rs, respectively. The ratio (rs / ra) is .

Question

An α-particle (mass 4 amu ) and a singly charged sulfur ion (mass 32 amu ) are initially at rest. They are accelerated through a potential V and then allowed to pass into a region of uniform magnetic field which is normal to the velocities of the particles. Within this region, the α-particle and the sulfur ion move in circular orbits of radii rα and rs, respectively. The ratio (rs / ra) is . (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

r a =(√2 m a q a V / q a B ) r S =(√2 m S q s V / q s B ) ( r S / r a) =√( m s / q S ) ( q a/ m a )=√((32/1))((2/4)) ( r s / r a) =4

ra​=qa​B2ma​qa​V​​ rS​=qs​B2mS​qs​V​​ ra​rS​​=qS​ms​​ma​qa​​​=(132​)(42​)​ ra​rs​​=4

$r_{a} = \frac{2 m _{a} q _{a} V}{q _{a} B}$
$r_{S} = \frac{2 m _{S} q _{s} V}{q _{s} B}$
$\frac{r _{S}}{r _{a}} = \frac{m _{s}}{q _{S}} \frac{q _{a}}{m _{a}} = (\frac{32}{1}) (\frac{2}{4})$
$\frac{r _{s}}{r _{a}} = 4$