Half Life Series Calculator
Free Half life series Calculator for nuclear chemistry. Enter variables to compute results with formulas and detailed steps.
Reviewed by Manoj Kumar, Mathematics Educator
Formula
N(t) = N0 x (1/2)^(t / t1/2)
The remaining amount N(t) equals the initial amount N0 multiplied by one-half raised to the power of elapsed time divided by the half-life. Each half-life period reduces the remaining amount by exactly 50%.
Worked Examples
Example 1: Iodine-131 Decay
Problem:Starting with 100 mg of I-131 (half-life 8.02 days), how much remains after 24 days?
Solution:Half-lives = 24 / 8.02 = 2.993\nN = 100 x (0.5)^2.993\nN = 100 x 0.1256\nN = 12.56 mg
Result:12.56 mg remaining (87.44% decayed)
Example 2: Drug Elimination
Problem:A drug with half-life 6 hours starts at 500 mg dose. How much is left after 1 day?
Solution:Half-lives = 24 / 6 = 4\nN = 500 x (0.5)^4\nN = 500 x 0.0625\nN = 31.25 mg
Result:31.25 mg remaining (93.75% eliminated)
Frequently Asked Questions
What is a half-life series?
A half-life series shows the progressive decay of a radioactive substance over successive half-life periods. After one half-life, 50% remains. After two half-lives, 25% remains. After three, 12.5%, and so on. Each half-life reduces the remaining amount by exactly half, following the exponential decay formula N(t) = N0 x (1/2)^(t/t1/2). This geometric progression is fundamental to understanding radioactive decay, pharmacokinetics, and any process that follows first-order kinetics.
How many half-lives until a substance is gone?
Mathematically, a substance never completely disappears through exponential decay. However, after 10 half-lives, only about 0.1% remains (1/1024 of the original). After 20 half-lives, less than 0.0001% remains. In practical terms, after about 7 half-lives (less than 1% remaining), the substance is often considered effectively eliminated. In pharmacology, drugs are considered cleared after 5 half-lives when about 97% has been eliminated from the body.
What is a radioactive decay series or decay chain?
A radioactive decay chain is a sequence of radioactive decays where a parent isotope decays into a daughter isotope, which is itself radioactive and decays further. This continues until a stable isotope is reached. The three natural decay series start with Uranium-238 (ending at Lead-206), Uranium-235 (ending at Lead-207), and Thorium-232 (ending at Lead-208). Each step in the chain has its own half-life and decay mode (alpha, beta, or gamma).
How is half-life used in carbon dating?
Carbon-14 dating uses the known half-life of C-14 (5,730 years) to determine the age of organic materials. Living organisms continuously exchange carbon with the environment, maintaining a constant C-14 ratio. After death, C-14 decays without replacement. By measuring the remaining C-14 ratio and applying the half-life formula, scientists calculate the time since death. This method is reliable for materials up to about 50,000 years old, which represents roughly 8-9 half-lives of C-14.
References
Reviewed by Manoj Kumar, Mathematics Educator · Editorial policy