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${H^ + },\,H{e^ + }$ and ${O^{ + + }}$ ions having same kinetic energy pass through a region of space filled with uniform magnetic field $B$ directed perpendicular to the velocity of ions. The masses of the ions ${H^ + },\,H{e^ + }$and ${O^{ + + }}$ are respectively in the ratio $1:4:16$. As a result
${H^ + }$ ions will be deflected most
${O^{ + + }}$ ions will be deflected least
$H{e^ + }$ and ${O^{ + + }}$ ions will suffer same deflection
Both $(a)$ and $(c)$
Solution
(d) $r \propto \frac{{\sqrt m }}{q}$$ \Rightarrow {r_H}:{r_{He}}:{r_o} = \frac{{\sqrt 1 }}{1}:\frac{{\sqrt 4 }}{1}:\frac{{\sqrt {16} }}{2} = 1:2:2$
Radius is smallest for ${H^ + }$, so it is deflected most.
Similar Questions
A charged particle (electron or proton) is introduced at the origin $(x=0, y=0, z=0)$ with a given initial velocity $\overrightarrow{\mathrm{v}}$. A uniform electric field $\overrightarrow{\mathrm{E}}$ and magnetic field $\vec{B}$ are given in columns $1,2$ and $3$ , respectively. The quantities $E_0, B_0$ are positive in magnitude.
|
column $I$ |
column $II$ | column $III$ |
| $(I)$ Electron with $\overrightarrow{\mathrm{v}}=2 \frac{\mathrm{E}_0}{\mathrm{~B}_0} \hat{\mathrm{x}}$ | $(i)$ $\overrightarrow{\mathrm{E}}=\mathrm{E}_0^2 \hat{\mathrm{Z}}$ | $(P)$ $\overrightarrow{\mathrm{B}}=-\mathrm{B}_0 \hat{\mathrm{x}}$ |
| $(II)$ Electron with $\overrightarrow{\mathrm{v}}=\frac{\mathrm{E}_0}{\mathrm{~B}_0} \hat{\mathrm{y}}$ | $(ii)$ $\overrightarrow{\mathrm{E}}=-\mathrm{E}_0 \hat{\mathrm{y}}$ | $(Q)$ $\overrightarrow{\mathrm{B}}=\mathrm{B}_0 \hat{\mathrm{x}}$ |
| $(III)$ Proton with $\overrightarrow{\mathrm{v}}=0$ | $(iii)$ $\overrightarrow{\mathrm{E}}=-\mathrm{E}_0 \hat{\mathrm{x}}$ | $(R)$ $\overrightarrow{\mathrm{B}}=\mathrm{B}_0 \hat{\mathrm{y}}$ |
| $(IV)$ Proton with $\overrightarrow{\mathrm{v}}=2 \frac{\mathrm{E}_0}{\mathrm{~B}_0} \hat{\mathrm{x}}$ | $(iv)$ $\overrightarrow{\mathrm{E}}=\mathrm{E}_0 \hat{\mathrm{x}}$ | $(S)$ $\overrightarrow{\mathrm{B}}=\mathrm{B}_0 \hat{\mathrm{z}}$ |
($1$) In which case will the particle move in a straight line with constant velocity?
$[A] (II) (iii) (S)$ $[B] (IV) (i) (S)$ $[C] (III) (ii) (R)$ $[D] (III) (iii) (P)$
($2$) In which case will the particle describe a helical path with axis along the positive $z$ direction?
$[A] (II) (ii) (R)$ $[B] (IV) (ii) (R)$ $[C] (IV) (i) (S)$ $[D] (III) (iii)(P)$
($3$) In which case would be particle move in a straight line along the negative direction of y-axis (i.e., more along $-\hat{y}$ )?
$[A] (IV) (ii) (S)$ $[B] (III) (ii) (P)$ $[C]$ (II) (iii) $(Q)$ $[D] (III) (ii) (R)$
