Decay Constant Calculator
Calculate decay constant with our free science calculator. Uses standard scientific formulas with unit conversions and explanations.
Reviewed by Manoj Kumar, Mathematics Educator
Formula
lambda = ln(2) / t(1/2)
The decay constant equals the natural logarithm of 2 (0.693147) divided by the half-life. Alternatively, it can be calculated from measured decay data using lambda = -ln(N(t)/N0) / t.
Worked Examples
Example 1: Carbon-14 Decay Constant
Problem:Calculate the decay constant of Carbon-14 with a half-life of 5,730 years.
Solution:lambda = ln(2) / t(1/2)\nlambda = 0.693147 / 5730\nlambda = 1.2097 x 10^-4 per year
Result:Decay constant = 1.2097 x 10^-4 per year
Example 2: Finding Decay Constant from Measurement
Problem:A sample of 1000 atoms decayed to 750 atoms in 2 hours. Find the decay constant.
Solution:lambda = -ln(750/1000) / 2\nlambda = -ln(0.75) / 2\nlambda = 0.2877 / 2 = 0.1438 per hour\nHalf-life = 0.693 / 0.1438 = 4.82 hours
Result:Decay constant = 0.1438 per hour, Half-life = 4.82 hours
Frequently Asked Questions
What is the decay constant?
The decay constant (lambda) is a probability rate that describes how quickly a radioactive substance undergoes nuclear decay. It represents the fraction of atoms that decay per unit time. A larger decay constant means faster decay and a shorter half-life. The relationship between decay constant and half-life is lambda = ln(2) / t(1/2), where ln(2) is approximately 0.693. The decay constant is an intrinsic property of each radioactive isotope and cannot be changed by chemical or physical means.
What is the relationship between decay constant and half-life?
The decay constant and half-life are inversely proportional: lambda = ln(2) / t(1/2). The half-life is the time required for half of a radioactive sample to decay. If the half-life is short, the decay constant is large and the substance decays rapidly. For example, Carbon-14 has a half-life of 5,730 years giving a decay constant of 1.21 x 10^-4 per year, while Polonium-214 has a half-life of only 164 microseconds with a much larger decay constant.
How is the decay constant used in radioactive dating?
In radioactive dating, the decay constant allows scientists to calculate the age of materials. By measuring the ratio of remaining parent isotope to daughter isotope, and knowing the decay constant, the age can be determined using t = -ln(N/N0) / lambda. Carbon-14 dating uses the known decay constant of C-14 to date organic materials up to about 50,000 years old. Uranium-lead dating uses the decay constants of U-238 and U-235 to date rocks billions of years old.
References
Reviewed by Manoj Kumar, Mathematics Educator · Editorial policy