Solved: PHYSICS Question for NEET

NEET PHYSICSEasy

Ionized hydrogen atoms and $\alpha$ -particles with the same momenta enter perpendicular to a constant magnetic field, $B$ . The ratio of their path radii $r_H : r_\alpha$ will be:

1 : 4

2 : 1

1 : 2

4 : 1

Step-by-Step Solution

Radius Formula: The radius ( $r$ ) of the circular path of a charged particle moving perpendicular to a uniform magnetic field ( $B$ ) is given by the equation: $r = \frac{mv}{qB} = \frac{p}{qB}$ where $m$ is mass, $v$ is velocity, $q$ is charge, and $p = mv$ is momentum .
Proportionality: Since the momentum ( $p$ ) and the magnetic field ( $B$ ) are the same for both particles, the radius is inversely proportional to the charge ( $q$ ). $r \propto \frac{1}{q}$
Particle Charges:

Ionized Hydrogen atom ( $H^+$ ) has a charge $q_H = +e$ .
$\alpha$ -particle ( $He^{2+}$ ) has a charge $q_\alpha = +2e$ .

Calculation: $\frac{r_H}{r_\alpha} = \frac{q_\alpha}{q_H} = \frac{2e}{e} = \frac{2}{1}$ Thus, the ratio is 2:1.

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