A mass spectrometer is used to separate isotopes of carbon, as shown in the diagram below.

A mixture of ${}^{12}{C}^{+}$ and ${}^{14}{C}^{+}$ ions is first passed through a velocity selector, where a uniform vertical electric field and a uniform magnetic field (pointing into the page) allow only ions of a specific velocity $v_0$ to emerge through the exit slit.

The ions then enter a deflection chamber containing only the uniform magnetic field pointing into the page. They follow semicircular paths and strike a detector plane at a distance $D$ from the exit slit, where $D$ represents the diameter of their semicircular path.

If the ${}^{12}{C}^{+}$ ions strike the detector at a distance $D_{12}$ from the exit slit, at what distance $D_{14}$ do the ${}^{14}{C}^{+}$ ions strike the detector?

Assume the mass of ${}^{12}{C}^{+}$ is $12u$, the mass of ${}^{14}{C}^{+}$ is $14u$, and both isotopes are singly-ionized with charge $+e$.