What is the relationship between the wavelengths of the energy absorbed by an object and the wavelengths reradiated? In other words, would the wavelengths of absorbed energy on an object be longer, shorter, equivalent, to the wavelengths reradiated on the object.
 A: The frequency spectrum radiated by a body is on general lines the black body radiation

Note it is a function of the temperature only. Here are more curves. The experimental curves may show deviations from the theoretical, but are more or less followed. The radiation from a body  as a function of frequency is just temperature dependent.
The opposite, the absorption of incoming radiation , is a complicated story as seen here.. Even though

There are a number of ways to quantify how quickly and effectively radiation is absorbed in a certain medium, for example:
The absorption coefficient, and some closely related derived quantities:
   The attenuation coefficient, which is sometimes but not always synonymous with the absorption coefficient

   Molar absorptivity, also called "molar extinction coefficient", which is the absorption coefficient divided by molarity (see also Beer–Lambert law).

  The mass attenuation coefficient, also called "mass extinction coefficient", which is the absorption coefficient divided by density (see also mass attenuation coefficient).

  The absorption cross section and scattering cross-section are closely related to the absorption and attenuation coefficients, respectively.

  "Extinction" in astronomy is equivalent to the attenuation coefficient.

Penetration depth and skin effect,
Propagation constant, attenuation constant, phase constant, and complex wavenumber,
Complex refractive index and extinction coefficient,
Complex dielectric constant,
Electrical resistivity and conductivity.
Absorbance (also called "optical density") and optical depth (also called "optical thickness") are two related measures
All these quantities measure, at least to some extent, how well a medium absorbs radiation. However, practitioners of different fields and techniques tend to conventionally use different quantities drawn from the list above.

So there is no simple one to one relation between absorption and re-radiation.
So a body  radiated will re-radiate back according to the temperature it reaches . Of course there will also be reflection of the incoming frequencies (and refraction and attenuation within a transparent body).
