Final answer:
The particle needed to complete the nuclear reaction 222 Rn → 218 Po is an alpha particle (He). The resulting balanced nuclear equation is 222 Rn → 218 Po + 4 He with a significant amount of gamma ray energy released.
Step-by-step explanation:
The particle needed to complete the nuclear reaction 222 Rn → 218 Po is an alpha particle, which is represented by He. In alpha decay, a radioactive nucleus emits an alpha particle and transforms into a new nucleus with a mass number that is reduced by four units and an atomic number that is reduced by two units. Hence, we use subtraction (222 - 4 = 218 and 86 - 2 = 84) to identify the daughter isotope of polonium, 218 Po. The complete balanced nuclear equation for the decay of radon-222 by alpha particle emission is:
222 Rn → 218 Po + 4 He
86 84 2
This nuclear reaction also releases gamma ray energy, which although not much for a single atom, would result in a significant amount of energy if one mole of Rn atoms were to decay—approximately 4.9 × 107 kJ.