Half-Life Graph

Make printable half-life graphs for chemistry and physics tests.

Isotopes

Each curve is N = N₀ · (½)^(t / T½): half is left after one half-life, a quarter after two, and it never reaches zero. Mass and activity fall along the same curve. Half-lives are from NuDat 3, rounded as textbooks give them; carbon-14 uses the textbook 5,730 years (NuDat 3 now gives 5,700 ± 30). The daughter curve, N₀ − N, is offered for one isotope whose daughter is stable, as a percent, fraction or number of nuclei. Hide the names and the key says Isotope A, B and C, for students to tell apart by the half-lives they read off.

Isotope 1

Up the side Time in

Carbon-14: half-life 5,730 years, λ = 1.21 × 10⁻⁴ per year; beta decay to nitrogen-14
After 1 half-life (5,730 years): 50%
After 2 half-lives (11,460 years): 25%
After 3 half-lives (17,190 years): 12.5%

Guide lines 3 half-lives, times

Dashed lines at Labeled with

Curves Curves

Draw the curves Dots at each half-life Daughter curve (Nitrogen-14) Hide the names

Titles “Time (years)” · “Percent remaining (%)”

Chart title

x-axis title

y-axis title

x-axis 0 to 30000 · by 2000 · numbered every 2 · no label · plain ends

From

Count by

Numbers

Label at the right end

Left end

Right end

y-axis 0 to 100 · by 10 · numbered · no label · plain ends

From

Count by

Numbers

Label at the top end

Bottom end

Top end

Grid No minor gridlines

Minor gridlines

Saved presets stay in this browser.

Half-life graphs of radioactive decay

Half-Life Graph draws the decay curve of a radioactive isotope: how much is left against time, halving every half-life, so half remains after one half-life, a quarter after two and an eighth after three. Pick carbon-14, hydrogen-3, fluorine-18, phosphorus-32, cobalt-60, strontium-90, technetium-99m, iodine-131, cesium-137, radon-222, radium-226, polonium-210, uranium-238, potassium-40, plutonium-239, americium-241 or a made-up Isotope X, or type your own name and half-life. Show the percent or fraction remaining, the mass from a starting mass, the number of nuclei or the activity in Bq or counts per minute, against time in the unit you choose.

Teachers use it for reading a half-life off a graph and working out how much is left. The x-axis counts in round steps, so students find the half-life from the curve; add dashed guide lines at the first one to four half-lives, labeled with their times, as T½, 2T½…, or with blank lines. Put up to three isotopes on one graph with their names hidden, for students to identify from their half-lives, draw a stable daughter rising as the parent falls, or leave only the dots for students to draw the curve. The answer key gives each half-life and decay constant.

What you can set

Up to three isotopes: 16 real ones with their half-lives, a made-up Isotope X, or your own name, half-life and unit
Up the side: percent remaining, fraction remaining, mass, number of nuclei, or activity in Bq or counts per minute, from the starting amount you type
Time in seconds, minutes, hours, days, years, thousand years or billion years, with the axes fitted to five half-lives in round steps
Dashed guide lines at the first 1 to 4 half-lives, labeled with their times, T½, 2T½…, blank lines or nothing
Dots at each half-life, the curves hidden for students to plot, a stable daughter curve, and names hidden as Isotope A, B and C
Color or black and white curves, chart and axis titles (or blank lines), the axis ranges and numbering, gridlines, and label size

Copying, printing and sharing

Copy the figure straight into a test, worksheet or slide, or download it as a PNG or SVG. Printing the page prints just the figure. Share link copies the page’s address with your settings in it, so anyone who opens it sees this exact figure, and presets save settings you use often in your browser. It’s free, with no sign-up.

Example figures

Carbon-14 half-life graph
Identify the isotope from its half-life: three decay curves
Carbon-14 decaying to nitrogen-14: parent and daughter
Iodine-131 decay: mass remaining over 45 days
Technetium-99m activity: read the half-life
Plot the decay curve: Isotope X, half-life 10 years

Frequently asked questions

How do you find the half-life from a graph?

Find half the starting amount on the y-axis (50% on a percent graph), go across to the curve and down to the time axis: that time is the half-life. Going from 50% to 25%, or 25% to 12.5%, takes the same time again. The guide lines draw exactly this, for one to four half-lives.

Why is carbon-14’s half-life 5,730 years and not 5,700?

Most textbooks and exam boards use 5,730 years, so the generator does too. The current evaluated value, in the National Nuclear Data Center’s NuDat 3, is 5,700 ± 30 years. To use it, choose Custom, name it carbon-14 and type 5700 years.

Where do the half-lives come from?

From NuDat 3, the National Nuclear Data Center’s database, rounded to three significant figures as textbooks give them: iodine-131 8.02 days, cesium-137 30.1 years, uranium-238 4.47 billion years. Carbon-14 uses the textbook 5,730 years.

Can it show the daughter isotope?

Yes, for one isotope whose daughter is stable, such as carbon-14 to nitrogen-14 or uranium-238 to lead-206, shown as a percent, fraction or number of nuclei. The daughter rises as the parent falls, and the two cross at one half-life. Strontium-90, radon-222, radium-226 and potassium-40 decay to radioactive daughters, so they don’t get one.

Can I compare isotopes on one graph?

Yes, up to three, drawn solid, dashed and dotted so they read apart in black and white, with a key under the graph. Hide the names and the key calls them Isotope A, B and C, for students to identify from their half-lives; the answer key names them.

Does the curve ever reach zero?

No. Each half-life leaves half of what was there, so the curve gets closer and closer to zero without reaching it: after ten half-lives about 0.1% is left.

← All chemistry figures