• summary_type: application
• word_count: 150

Radioactive dating exploits known half-lives to determine age. Carbon-14 dating: living organisms maintain constant C-14/C-12 ratio via atmospheric exchange. After death, C-14 decays (t_(1/2) = 5730 years). Age = (t_(1/2)/0.693)*ln(A_0/A), where A_0 is initial activity and A is current activity. Effective range: ~50,000 years. For geological timescales, uranium-lead dating uses U-238 (t_(1/2) = 4.5 x 10^9 years) decaying to Pb-206. If N_Pb lead atoms and N_U uranium atoms are found: age = (1/lambda)*ln(1 + N_Pb/N_U). JEE problems typically give a ratio (like "activity drops to 1/4 of initial") and ask for age in terms of half-life: if A/A_0 = 1/4, then 2 half-lives have passed. For non-power-of-2 ratios, use the logarithmic formula. Potassium-argon dating (K-40, t_(1/2) = 1.28 x 10^9 years) is used for volcanic rocks.