Net Effects of β and α Decay on Nucleon and Proton Numbers

Steps:

• Actinium starts with nucleon number A=227 and proton number Z=89.
• β decay converts a neutron to a proton: A unchanged, Z increases by 1 (to 90).
• α decay emits a helium nucleus (A=4, Z=2): A decreases by 4, Z decreases by 2.
• Net changes: ΔA = 0 (β) - 4 (α) = -4; ΔZ = +1 (β) - 2 (α) = -1.
• Radium final: A=227-4=223, Z=89-1=88.

Why B is correct:

• Matches net decay formula: total mass loss of 4 nucleons and atomic number decrease of 1 from combined emissions.

Why the others are wrong:

• A: Correct A=223 but Z=87 ignores β's Z increase.
• C: A=224 subtracts only 3 nucleons; Z=87 ignores β effect.
• D: A=225 subtracts only 2 nucleons; Z=86 subtracts 3 protons.

Final answer: B