Question

Two ions of masses $4$ amu and $16 $ amu have charges $+2 e$ and $+3 e$ respectively. These ions pass through the region of constant perpendicular magnetic field. The kinetic energy of both ions is same. Then:

• A. lighter ion will be deflected less than heavier ion
• B. lighter ion will be deflected more than heavier ion
• C. both ions will be deflected equally
• D. no ion will be deflected.

Answer 1

Answer: (B)

$r=\frac{P}{q B}=\frac{\sqrt{2 m k}}{q B}$
Given they have same kinetic energy
$r \propto \frac{\sqrt{m}}{q}$
$\frac{r_{1}}{r_{2}}=\frac{\sqrt{4}}{2} \times \frac{3}{\sqrt{16}}=\frac{3}{4}$
$r _{2}=\frac{4 r _{1}}{3}$
( $r _{2}$ is for hearier ion and $r _{1}$ is for lighter ion)

$\sin \theta=\frac{d}{R}$
$\theta \rightarrow$ Deflection
$\theta \propto \frac{1}{R}$
$(R \rightarrow$ Radius of path)
$\because R_{2}>R_{1}$
$ \Rightarrow \theta_{2}<\theta_{1}$