Elements that appear in the same column of the periodic table often share similar chemical properties. For alkaline earth metals,

this is troublesome because the body treats radium $($a radioactive element$)$ like calcium, storing it in the bone marrow. The

radium then bombards nearby bone cells with alpha particles, causing them to "crumble."

Radium poisoning investigations often center on the identification of radium and its isotopes in bone samples using a mass

spectrometer. Pictured is a schematic of a simplified mass spectrometer that shows the paths of calcium isotopes, barium

$($another alkaline earth metal$)$ isotopes, and radium isotopes entering the chamber.

The region shown is immersed in a constant magnetic field of

$0\mathrm{.}352T$ pointing out of the plane of the schematic. Motion of

the positively$-$charged isotopes toward the right was initiated

by a potential difference of $3082V$ on the two plates shown.

The table lists the mass and charge of each isotope detected

by the mass spectrometer.

Using the data shown in the table, calculate the path radius $r$

of the $C{a}^{+}$ion.

$r=$

Using the same data table, match the particles to their

path label.

Path A

Path B

Path C

Path D

Path E

Path F