In each of the following radioactive decay processes, supply the missing particle. a. \(^{73} \mathrm{Ga} \rightarrow^{73} \mathrm{Ge}+?\) b. \(^{192} \mathrm{Pt} \rightarrow^{188} \mathrm{Os}+?\) c. \(^{205} \mathrm{Bi} \rightarrow^{205} \mathrm{Pb}+?\) d. \(^{241} \mathrm{Cm}+? \rightarrow^{241} \mathrm{Am}\)

We'll first look at the atomic numbers (Z) and mass numbers (A) for each pair of elements. a. Ga (Z = 31, A = 73) and Ge (Z = 32, A = 73) b. Pt (Z = 78, A = 192) and Os (Z = 76, A = 188) c. Bi (Z = 83, A = 205) and Pb (Z = 82, A = 205) d. Cm (Z = 96, A = 241) and Am (Z = 95, A = 241)

Look at the decay process of each and determine the changes in the atomic numbers (ΔZ) and the mass numbers (ΔA). a. Ga to Ge: ΔZ = 1, ΔA = 0 b. Pt to Os: ΔZ = -2, ΔA = -4 c. Bi to Pb: ΔZ = -1, ΔA = 0 d. Cm to Am: ΔZ = -1, ΔA = 0

Identify the decay process based on the changes in atomic numbers and mass numbers, and find the missing particle that fulfills these changes. a. Ga to Ge: Since ΔZ = 1 and ΔA = 0, this indicates β- decay. The missing particle is an electron (e-) or β- particle. b. Pt to Os: Since ΔZ = -2 and ΔA = -4, this indicates α decay. The missing particle is an alpha particle, or a Helium-4 nucleus (\(^{4}\textrm{He}\)). c. Bi to Pb: Since ΔZ = -1 and ΔA = 0, this indicates β+ decay or electron capture (EC). The missing particle is a positron (e+) for β+ decay or an electron (e-) for electron capture. d. Cm to Am: Since ΔZ = -1 and ΔA = 0, this indicates neutron capture. The missing particle is a neutron (\(^{1}\textrm{n}\)).