• $summary_{type}$: 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_$\frac{1}{2}$ = 5730 years). Age = $\frac{t_(1/2}{0.693}$)*ln$\frac{A_0}{A}$, 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_$\frac{1}{2}$ = 4.5 x 10^9 years) decaying to Pb-206. If $N_{Pb}$ lead atoms and $N_U$ uranium atoms are found: age = $\frac{1}{lambda}$*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_$\frac{1}{2}$ = 1.28 x 10^9 years) is used for volcanic rocks.