Two Electrons Are Placed into Separate (Very Tiny) One-Dimensional Boxes $A$

Multiple Choice

Two electrons are placed into separate (very tiny) one-dimensional boxes $A$ and $B$ . When the electrons are excited to higher energy levels and then decay to lower levels, they emit photons. The longest-wavelength spectral line from the electron in box $A$ is observed to have the same wavelength as the third-longest spectral line from the electron in box
$B$ . The ratio of the box lengths $L_{A} / L_{B}$ is equal to

A) $3 / 7$
B) $7 / 3$
C) $\sqrt{3 / 7}$
D) $\sqrt{7 / 3}$
E) $9 / 49$