Asked by Victoria Cuevas on Mar 10, 2024



Radioactive carbon, 14C{ } ^ { 14 } \mathrm { C }14C , has a has a half-life of 5730 years. After 1000 years, 3.7 grams remain. What was the initial quantity of 14C{ } ^ { 14 } \mathrm { C }14C ? Round your answer to two decimal places.

A) 4.18 grams
B) 3.90 grams
C) 4.35 grams
D) 6.98 grams
E) 3.94 grams


Half-life is a term used in nuclear physics and chemistry to describe the time required for one half of the atoms of a radioactive substance to undergo decay.

  • Apply the exponential model to solve real-world problems related to finance and physical sciences.
  • Gain proficiency in the application of exponential growth and decay concepts in multiple contexts, encompassing population growth and the diminishment of radioactivity.

Verified Answer

Lindsays LaFontaine

Mar 10, 2024

Final Answer :
Explanation :
The amount of radioactive carbon remaining after a certain period can be calculated using the formula A=A0(12)tTA = A_0 \left(\frac{1}{2}\right)^{\frac{t}{T}}A=A0(21)Tt , where AAA is the amount remaining, A0A_0A0 is the initial amount, ttt is the time elapsed, and TTT is the half-life. Rearranging to solve for A0A_0A0 , we get A0=A(12)−tTA_0 = A \left(\frac{1}{2}\right)^{-\frac{t}{T}}A0=A(21)Tt . Substituting A=3.7A = 3.7A=3.7 grams, t=1000t = 1000t=1000 years, and T=5730T = 5730T=5730 years, we find A0≈4.18A_0 \approx 4.18A04.18 grams.