• summary_type: application
• word_count: 150

In a decay chain A -> B -> C, the rate equation for B is dN_B/dt = lambda_AN_A - lambda_BN_B. In secular equilibrium (when t_(1/2) of A >> t_(1/2) of B): lambda_AN_A = lambda_BN_B, meaning activities are equal throughout the chain. The natural radioactive series: U-238 series (A = 4n+2, ends at Pb-206, 14 decays: 8 alpha + 6 beta), U-235 series (A = 4n+3, ends at Pb-207), Th-232 series (A = 4n, ends at Pb-208). To find the number of alpha and beta decays: alpha count = (A_initial - A_final)/4, then beta count is determined by balancing Z. For the U-238 -> Pb-206 series: alpha count = (238-206)/4 = 8, Z change from alpha alone = -16, actual Z change = 82-92 = -10, so beta-minus count = -16-(-10) = 6.