Half-Life Calculator
Half-Life Calculator Online – Easily Calculate Radioactive Decay
Intro
A Half-Life Calculator online is a simple yet powerful tool designed to calculate how long it takes for a substance to decay to half of its original amount. This concept is commonly used in physics, chemistry, biology, archaeology, and even medicine. Instead of performing complex equations manually, the Half-Life Calculator provides quick and accurate results in seconds.
Whether you are a student learning about radioactive decay, a researcher studying isotopes, or simply curious about how substances lose mass over time, this tool saves time and ensures accuracy. By using the calculator, anyone can easily determine the remaining quantity of a substance after a certain number of half-lives.
Formula / Working
The Half-Life Calculator uses the standard exponential decay formula: N(t)=N0×(12)tT1/2N(t) = N_0 \times \left(\frac{1}{2}\right)^{\frac{t}{T_{1/2}}}N(t)=N0×(21)T1/2t
Where:
- N(t) = Amount of substance left after time t
- N₀ = Initial amount of substance
- T₁/₂ = Half-life of the substance
- t = Time elapsed
The formula shows that after each half-life, only half of the substance remains. For example, if a radioactive isotope has a half-life of 10 years, then after 10 years half remains, after 20 years a quarter remains, and so on.
Step-by-Step Usage
Using the Half-Life Calculator is quick and simple:
- Enter the initial amount of the substance (N₀).
- Input the half-life value (T₁/₂) of the substance.
- Enter the time elapsed (t).
- Click the Calculate button.
- The calculator will display the remaining amount (N(t)).
This step-by-step process eliminates the need for manual calculations, making it user-friendly for students, professionals, and researchers.
Examples
Example 1: Carbon-14 Dating in Archaeology
- Initial amount (N₀): 100 grams
- Half-life of Carbon-14 (T₁/₂): 5730 years
- Time elapsed (t): 11,460 years
N(t)=100×(12)114605730N(t) = 100 \times \left(\frac{1}{2}\right)^{\frac{11460}{5730}}N(t)=100×(21)573011460 N(t)=100×(12)2=25 gramsN(t) = 100 \times \left(\frac{1}{2}\right)^2 = 25 \text{ grams}N(t)=100×(21)2=25 grams
✅ After 11,460 years, only 25 grams of Carbon-14 remains.
Example 2: Medical Use – Radioactive Tracer
- Initial amount (N₀): 80 mg
- Half-life (T₁/₂): 6 hours
- Time elapsed (t): 18 hours
N(t)=80×(12)186N(t) = 80 \times \left(\frac{1}{2}\right)^{\frac{18}{6}}N(t)=80×(21)618 N(t)=80×(12)3=10 mgN(t) = 80 \times \left(\frac{1}{2}\right)^3 = 10 \text{ mg}N(t)=80×(21)3=10 mg
✅ After 18 hours, only 10 mg of the tracer remains in the body.
Example 3: Nuclear Waste Decay
- Initial amount (N₀): 500 g
- Half-life (T₁/₂): 30 years
- Time elapsed (t): 90 years
N(t)=500×(12)9030N(t) = 500 \times \left(\frac{1}{2}\right)^{\frac{90}{30}}N(t)=500×(21)3090 N(t)=500×(12)3=62.5 gN(t) = 500 \times \left(\frac{1}{2}\right)^3 = 62.5 \text{ g}N(t)=500×(21)3=62.5 g
✅ After 90 years, only 62.5 grams of nuclear material remains.
FAQs
1. What is a Half-Life Calculator?
A Half-Life Calculator is an online tool that helps you calculate the remaining amount of a substance after a certain period of time using its half-life value.
2. How does the Half-Life Calculator work?
It applies the exponential decay formula to determine how much of the substance remains after a given time.
3. Why should I use a Half-Life Calculator online?
It saves time, ensures accuracy, and is useful for students, teachers, researchers, and professionals in medicine, archaeology, and nuclear studies.
4. Is the Half-Life Calculator free to use?
Yes, most Half-Life Calculators online are completely free and available to anyone.
5. Can I use the Half-Life Calculator on mobile?
Yes, the tool is mobile-friendly and can be accessed from any smartphone, tablet, or computer with an internet connection.