Are the products of nuclear fission radioactive?

The daughter atoms from nuclear fission are nearly always radioactive and nearly always have very short half lives decaying through chains of atoms of short half lives. There is a reason for this.

We do not know exactly what the daughter atoms from the fission of a given atom will be, but we do know they will contain all the protons of the parent. The number of neutrons is also preserved, though a few unbound neutrons are usually emitted from the fission. Since atoms with higher atomic numbers can have a greater proportion of protons to neutrons, the daughters usually have far too many neutrons to be stable, and will usually undergo negative beta decay. For example, the fission of ²³⁵U might look like this:

₉₂²³⁵U --> ₃₆⁹²Kr + ₅₆¹⁴¹Ba + 2n

The most massive stable isotope of krypton is ⁸⁶Kr, so our daughter krypton atom has six too many neutrons to be stable. The decay chain of the ⁹²Kr, given as isotopes and half lives, is as follows, with all decays by negative beta decay:

⁹²Kr 1.8 seconds
⁹²Rb 4.5 seconds
⁹²Sr 2.71 hours
⁹²Y 3.54 hours
⁹²Zr stable

The most massive stable isotope of barium is ¹³⁸Ba, so our daughter has three too many neutrons to be stable. The decay chain of the ¹⁴¹Ba similar to the above is as follows, again all by negative beta decay:

¹⁴¹Ba 18.27 minutes
¹⁴¹La 3.92 hours
¹⁴¹Ce 32.5 days
¹⁴¹Pr stable

Most of the daughter decay chains do not produce stable isotopes nearly as quickly as the above, with many having products with half lives of decades to millennia. By comparison, our parent atom, ²³⁵U, had a half life of 703,800,000 years.