Ionized hydrogen atoms and alpha-particles wi | vedclass

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(A) The radius of a charged particle moving in a magnetic field is given by $r = \frac{mv}{qB} = \frac{p}{qB}$,where $p$ is the momentum,$q$ is the ch

Vedclass · Accepted Answer

$2:1$

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(A) The radius of a charged particle moving in a magnetic field is given by $r = \frac{mv}{qB} = \frac{p}{qB}$,where $p$ is the momentum,$q$ is the charge,and $B$ is the magnetic field.Given that the momenta $p$ and the magnetic field $B$ are the same for both particles,the radius is inversely proportional to the charge: $r \propto \frac{1}{q}$.For an ionized hydrogen atom (proton),the charge is $q_{H} = +e$.For an $\alpha$-particle (helium nucleus),the charge is $q_{\alpha} = +2e$.Therefore,the ratio of the radii is $\frac{r_{H}}{r_{\alpha}} = \frac{q_{\alpha}}{q_{H}} = \frac{2e}{e} = \frac{2}{1}$.Thus,the ratio $r_{H}: r_{\alpha}$ is $2:1$.

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

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