Question

The half-life for the radioactive decay of C−14 is 5730 years.

A) How long will it take for 30% of the C−14 atoms in a sample of C−14 to decay?

B) If a sample of C−14 initially contains 1.9 mmol of C−14, how many millimoles will be left after 2280 years?

Answer 1

A) Radio active decay follows the 1st order kinetics Half lifeperiod of carbon -14, t 5730 years 0693121x10* years 5730 years 0.693 Rate constant, _ - Initi al amount of C-14 -[Al, amount of C-14 left after time t , A,-A,-30%A,-0.7014, According to 1st order kinetics, t --ln O A] Age of bones In 1.21x10 years 0.70A = 2948 years B) Initi al amount of C-14 ,A9 mol amount of C-14 left after time t [A time elapsed 2280 year Rate constant, k = 1.21×10-years- According to 1st order kinetics, k --In 1.21x10* years280 year[A 19 mmol 0.27588 1.9 mmol- 1.318 1.9 mmol In -1 In [A 1.9 mmol - 14mmol [A 1.318