Question

Two ions of masses $4$ amu and $16$ amu have charges $+2e$ and $+3e$ 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)

$r=\frac{P}{qB}=\frac{\sqrt{2mk}}{qB}$
Given they have same kinetic energy
$r\propto \frac{\sqrt{m}}{q}$
$\frac{r_1}{r_2}=\frac{\sqrt{4}}{2}\times \frac{3}{\sqrt{16}}=\frac{3}{4}$
$r_2=\frac{4r_1}{3}$
( $r_2$ is for hearier ion and $r_1$ is for lighter ion)

$\sin \theta =\frac{d}{R}$
$\theta \to$ Deflection
$\theta \propto \frac{1}{R}$
$(R\to$ Radius of path)
$\because R_2>R_1$
$\Rightarrow {\theta }_2<{\theta }_1$