Half-Life Calculator

Formula

The formula to calculate half-life is:

\[ t_{1/2} = \frac{t \cdot \log(2)}{\log \left( \frac{N_0}{N(t)} \right)} \]

Where:

\( t_{1/2} \) is the half-life
\( N_0 \) is the initial quantity
\( N(t) \) is the remaining quantity after time \( t \)
\( t \) is the time elapsed

What is Half-Life?

A half-life is the time it takes for a given substance to deteriorate or lose half of its mass. The term is primarily used in nuclear physics to describe the rate of decay of radioactive substances. It is an important concept in various scientific fields, including chemistry, pharmacology, and environmental science.

Example Calculation

Let's assume the following values:

Initial Quantity (N0): 100 grams
Remaining Quantity (N(t)): 25 grams
Time Elapsed (t): 10 years

Step 1: Calculate the Half-Life:

\[ t_{1/2} = \frac{10 \cdot \log(2)}{\log \left( \frac{100}{25} \right)} = \frac{10 \cdot 0.693}{\log(4)} = \frac{6.93}{1.386} = 5 \text{ years} \]

Therefore, the half-life is 5 years.