Here it says to write a balanced nuclear reaction for beta decay of iodine 129. All right, so iodine 129. If we look on the periodic table, iodine has an atomic number of 53 beta. Decay means that our energetic particle, in this case the electron, will be a product.
Remember the mass numbers on both sides have to be the same. The total number of protons on both sides have to be the same. Here this would still be 129 because 129 + 0 gives me 129. On the reactant side we have 53 protons, so on the product side we also need 53 protons. The number here would have to be 54 because 54 - 1 gives me 53.
Now if we look on the periodic table, what element has an atomic number of 54? That's right, it will be xenon. So here we'd say that iodine 129 turns into xenon 129 by way of beta decay. So this will represent our beta decay reaction of iodine 129.
I 129 → Xe 129 + e -