solar system - What wavelength to best detect the "9th planet"?

There are two basic ways to detect such an object. First is to detect it through reflected sunlight. Second is from the heat that it produces. We already know that the reflected light of such an object likely would be around a 16.5 magnitude. To determine the infrared, we have to estimate the temperature

The temperature very much depends on the composition. For simplicity, let's assume a composition similar to Earth, and was created about the same time as the rest of the Solar System. These assumptions may not prove to be valid, but they are among the possibilities discussed. Earth's internal heat, in fact, is at least 50% from radioactive decay, according to Scientific America. Of course, that's the internal heat only, not all of that will make it to the surface.

This proposed planet is somewhat akin to a "Rogue Planet", where a small disk of gas collapsed into a planet without a star, or were ejected from their host system. A fair bit also depends on if there is a sizable moon of the object. If so, then tidal heating would dramatically increase the temperature of the object. Any such determination can't be made without observation, but it is possible. An atmosphere would also help to keep the planet from freezing. A paper for detecting rogue planets comes from Abbott and Switzer. They hypothesis that a 3.5 Earth Mass object could be detected if it comes within 1000 AU, specifically in the far infrared, with a surface temperature of about 50 K.

Bottom line, it would probably be wise to try to detect both in the far infrared, as well as the visible, although it might be difficult to detect, even then. Given parallax as the primary means of motion, the detection should be done at several points in Earth's orbit, probably the same spot should be searched about 90 days apart to give the maximum opportunity to move, as parallax would only be visible if the motion of the Earth was perpendicular to the location of the object.