Are the radiation wavelengths emitted by the sun longer than those emitted by the earth?

The radiation emitted by the Earth peaks around 10 microns, whereas that from the sun peaks under 1 micron. This is why Earth's radiation is referred to as longwave and solar radiation as shortwave, commonly.

All objects emit radiation because all objects have a temperature. In fact, using Wien's Law you can very simply calculate the wavelength, lambda, of maximum emission:

lamda(max) = c/T

where c is a constant (2897) and T is the temperature of the emitting surface in Kelvin.