Radioactivity and Nuclear Decay

Carbon-14 is a radioactive isotope of carbon with a half-life of approximately 5,730 years. This property makes it useful for radiocarbon dating of organic materials up to about 50,000-60,000 years old. The half-life is the time for half of the radioactive atoms to decay.

After 15 minutes, exactly 3 half-lives have passed (15/5 = 3). Each half-life reduces the amount by half, so after 3 half-lives: 1 gram * (1/2)^3 = 1 * 1/8 = 0.125 gram remains.

After 40 days (which is 4 half-lives of 10 days each), the remaining mass = 2g × (1/2)^4 = 2g × 1/16 = 0.125g. Each half-life reduces the quantity by half, so after n half-lives, remaining = initial × (1/2)^n.

Radioactive dating (also called radiometric dating) calculates the age of rocks, fossils, or archaeological materials by measuring the ratio of a radioactive isotope to its decay product. This relies on known half-lives - not the time for complete decay (which takes infinite time). It's different from radiation detection methods.

Ending Amount = Beginning Amount / 2^{(time / half-life)} Ending Amount = 200 / 2^(75/12.5) Ending Amount = 200 / 2⁽⁶⁾ Ending Amount = 200/64 Ending Amount = 3.125g  

Elapsed time = half life x log (beginning amount / ending amount) /log 2 Elapsed time = 91 x [log (100/10) / 0.30103] Elapsed time = 91 x (1/0.30103) Elapsed time = 27.4 days (approx).

disintegration per minute (dpm) = count per minute (cpm)/efficency. Therefore, cpm = dpm*efficency = 211326*97/100.

Disintegration per minute (dpm) = cpm/efficency = 134503/98.8*100 = 136136.6dpm.

Disintegration per minute (dpm)=cpm/efficency. Disintegration per second(dps) = dpm/60. Curie = Dps/3.7*10¹⁰.

Henri Becquerel discovered radioactivity in 1896 while studying uranium salts. He noticed they exposed photographic plates even in darkness, revealing that certain materials emit radiation spontaneously without external energy input.

Plutonium was first synthesized and identified in 1940 by a team led by Glenn T. Seaborg at the University of California, Berkeley. The discovery occurred during research on transuranium elements, specifically through the bombardment of uranium-238 with deuterons in a cyclotron.

Nuclear stability is primarily determined by the neutron-to-proton (N/P or n/p) ratio in the nucleus. Stable nuclei have optimal N/P ratios that balance nuclear forces. Too few or too many neutrons leads to instability and radioactivity. Half-life measures decay rate, not stability. P/N ratio is same as N/P but less common notation. R/n is not a standard concept.

Carbon-14 has a half-life of approximately 5,730 years, which is commonly rounded to 5,000 years in educational contexts for simplicity. 8,000 years is too long, and 19,000 years is far too long. The half-life is crucial because it determines the dating range (~50,000 years maximum) of radiocarbon dating.