A proton and an α-particle (with their masses in the ratio of 1: 4 and charges in the ratio of 1: 2) are accelerated from rest through a potential difference V. If a uniform magnetic field (B) is set up perpendicular to their velocities, the ratio of the radii rp: rα of the circular paths described by them will be :

Question

A proton and an α-particle (with their masses in the ratio of 1: 4 and charges in the ratio of 1: 2) are accelerated from rest through a potential difference V. If a uniform magnetic field (B) is set up perpendicular to their velocities, the ratio of the radii rp: rα of the circular paths described by them will be : (A) 1: √2 (B) 1: 2 (C) 1: 3 (D) 1: √3

Tardigrade Admin · Accepted Answer

KE =qΔ V r =(√2mqΔ V/qB) r propto √(m/q) (rp/r∞) = (1/√2)

$1 : 2$

$1 : 2$

$1 : 3$

$1 : 3$

$K E = q Δ V$
$r = \frac{2 m q Δ V}{qB}$
$r \propto \frac{m}{q}$
$\frac{r _{p}}{r _{\infty}} = \frac{1}{2}$

1:2​

1:2

1:3

1:3​

KE=qΔV r=qB2mqΔV​​ r∝qm​​ r∞​rp​​=2​1​

$1 : 2$

$1 : 2$

$1 : 3$

$1 : 3$

$K E = q Δ V$
$r = \frac{2 m q Δ V}{qB}$
$r \propto \frac{m}{q}$
$\frac{r _{p}}{r _{\infty}} = \frac{1}{2}$