Question 21.SE.2: Write nuclear equations for (a) mercury-201 undergoing elect...

Analyze We must write balanced nuclear equations in which the masses and charges of reactants and products are equal.

Plan We can begin by writing the complete chemical symbols for the nuclei and decay particles that are given in the problem.

Solve
(a) The information given in the question can be summarized as

{}_{80}^{201}Hg +{}_{-1}^0 e \longrightarrow{}_Z^A X

The mass numbers must have the same sum on both sides of the equation:

201 + 0 = A

Thus, the product nucleus must have a mass number of 201. Similarly, balancing the atomic numbers gives

80 – 1 = Z

Thus, the atomic number of the product nucleus must be 79, which identifies it as gold (Au):

{}_{80}^{201}Hg +{}_{-1}^0 e \longrightarrow{}_{79}^{201}Au

(b) In this case, we must determine what type of particle is emitted in the course of the radioactive decay:

{ }_{90}^{231} Th \longrightarrow{ }_{91}^{231} Pa +{ }_Z^A X

From 231 = 231 + A and 90 = 91 + Z, we deduce A = 0 and Z = -1. According to Table 21.2, the particle with these characteristics is the beta particle (electron). We therefore write

{}_{90}^{231}Th \longrightarrow{}_{91}^{231}Pa +{}_{-1}^0 e  \text{or}  {}_{90}^{231}Th \longrightarrow{}_{91}^{231}Pa +\beta^{-}