# Solving Half Life Problems While a radioactive isotope decays almost perfectly according to so-called "first order kinetics" where the rate constant is a fixed number, the elimination of a substance from a living organism usually follows more complex chemical kinetics.

The biological half-life of caesium in human beings is between one and four months.

Half-life is defined as the amount of time it takes a given quantity to decrease to half of its initial value.

Instead, the half-life is defined in terms of probability: "Half-life is the time required for exactly half of the entities to decay on average".

In other words, the probability of a radioactive atom decaying within its half-life is 50%.

The half-life of carbon-14 is approximately 5,730 years, and it can be reliably used to measure dates up to around 50,000 years ago.

## Solving Half Life Problems

The process of carbon-14 dating was developed by William Libby, and is based on the fact that carbon-14 is constantly being made in the atmosphere.

This is the exact solution; evaluate the natural log with a calculator to get the decimal approximation k = -0.000436 .

A typical "half-life problem" might be worded: Tungsten 181 has a λ value of 0.005723757/days. Half-Life = ln(2) ÷ λ Half-Life = .693147 ÷ 0.005723757 Half-Life = 121.1 days Scroll down for 4 more half-life problems.

## Comments Solving Half Life Problems

• ###### Half-Life and Activity – College Physics - BC Open Textbooks

Is reasonably large, half of the original nuclei decay in a time of one half-life. Solution. Solving the equation N={N}_{0}{e}^{-\ for N/{N}_{0} gives. Construct a problem in which you calculate the mass of a radioactive isotope you need in.…

• ###### HALF-LIFE EQUATIONS -

Half-Life Calculator, exponential decay, Radioactivity. A typical "half-life problem" might be worded. Scroll down for 4 more half-life problems. This might seem somewhat different than the other examples but all we have to do is let Nt = 5.…

• ###### Half-life - Wikipedia

There is a half-life describing any exponential-decay process. As noted above, in radioactive decay the half-life is the length of time.…

• ###### Example -- Exponential Decay

A radioactive substance is often described in terms of its half-life, which is the time. Problem. After 500 years, a sample of radium-226 has decayed to 80.4\% of. in the formula for exponential decay to be equal to 1/2A0, and then solve for t.…

• ###### How to Calculate Using Half Life Sciencing

Jul 22, 2019. You can use the half life equation to calculate how long radioactive waste will. Half Life Problems and Answers Examples Radioactive Waste.…

• ###### Untitled - Mayfield City Schools

Complete the following half-life problems be sure to show your thinking when solving problems. PROBLEM. If 100.0 g of carbon-14 decays until only 25.0 g of.…

• ###### How to solve Half Life problems in calculus - Quora

The other answer walks through how to think about deriving the continuous model for an instantaneous rate of decay mathk/math with.…

• ###### Half life practice problems Quiz - Quizizz

Play this game to review Nuclear Chemistry. What is Half-life?…