| title | description | author | layout | date | image |
|---|---|---|---|---|---|
Interactive Half-Life Calculator |
Slide sliders to get a feel for half-life. Calculate how much stuff is left after a few half-lives.
|
nick |
default |
2022-10-30 |
/img/half-life.jpg |
← less stable
Half-life (years)
more stable →
Half-life
Half-life Range
100
1,000
10 k
100 k
1 M
10 M
100 M
1 B
10 B
Max time to show (years)
Max time
Time Range
100
1,000
10 k
100 k
1 M
10 M
100 M
1 B
10 B
Number of bars
Number of bars
Log x axis
Show 50% mark
Log y axis
A thing's half-life is how long until only half of it is left. It's used in radioactive decay, medicine, and many other things. Remember:
- Hazards in radiation are proportional the rate at which energy comes out.
- Short half-lives imply energy is coming out quickly, and are the primary hazard.
- Long half-lives imply energy is coming out very slowly, and are less of a hazard. For example, you can hold long half-life isotopes of natural uranium in your hand without accumulating a hazardous dose.
- In the extreme, an infinite half-life would mean energy never comes out, representing zero radiological risk.
Learn more about [the math here]({% link math-behind-radioactive-decay.html %}).
This graph depicts a single nuclide with its single half-life decaying to stability. Nuclear waste is typically composed of thousands of different [nuclides]({% link isotopes.md %}) that each have their own unique half-life, and often decay to other radioactive daughter nuclides before making it to stability.
Learn about solutions to nuclear waste [here]({% link waste.md %}).
<script src='https://cdn.plot.ly/plotly-2.16.1.min.js'></script> <script> let halflife=document.getElementById("halflife"); let number=document.getElementById('value') let hl_range_select=document.getElementById('hl-range-select') let maxtime_range=document.getElementById("maxtime"); let maxtime_val=document.getElementById('maxtime-val') let time_range_select=document.getElementById('time-range-select') let numbars_range=document.getElementById("numbars-range"); let numbars_val=document.getElementById('numbars-val') let logx=document.getElementById('logx') let logy=document.getElementById('logy') let hlnote=document.getElementById('hlnote') halflife.addEventListener("input",(e)=>{ let val = parseFloat(e.target.value); if (val{ halflife.value=e.target.value; compute(); }) hl_range_select.addEventListener("change",(e)=>{ halflife.max=e.target.value; }) maxtime_range.addEventListener("input",(e)=>{ let val = parseFloat(e.target.value); if (val{ maxtime_range.value=e.target.value; compute(); }) time_range_select.addEventListener("change",(e)=>{ maxtime_range.max=e.target.value; }) numbars_range.addEventListener("input",(e)=>{ let val = parseFloat(e.target.value); if (val{ numbars_range.value=e.target.value; compute(); }) logx.addEventListener("input",(e)=>{ compute(); }) logy.addEventListener("input",(e)=>{ compute(); }) hlnote.addEventListener("input",(e)=>{ compute(); }) function compute() { let maxtime = Number(maxtime_val.value); let initial = 100; let numbars = Number(numbars_val.value); let halflife = Number(number.value); // if they want 10 bars between 0 and 100 years, // then the 10th bar with have index 9, and we need 9/10 let times = Array.from({length: numbars}, (x, i) => i*maxtime/(numbars-1)); let times2 = Array.from({length: 50}, (x, i) => i*maxtime/(50-1)); let dec_const = Math.log(2)/halflife; // update line data let line_vals = times2.map((time) => initial*Math.exp(-dec_const * time)) let line = { x: times2, y: line_vals, type: 'scatter', showlegend: false, marker: { "color": "black", } }; // update bars data let rvals = times.map((time) => initial*Math.exp(-dec_const * time)) let radioactive = { x: times, y: rvals, text: rvals.map((val) => String(val.toFixed(1))), name: 'Still radioactive', type: 'bar', marker: { "color": "firebrick", "pattern": { "solidity": 0.5 } } }; let decayed = { x: times, y: times.map((time) => initial*(1-Math.exp(-dec_const * time))), name: 'No longer radioactive', type: 'bar', marker: { "color": "burlywood", "pattern": { "shape": "x", "solidity": 0.5 } } }; /* if (numbars>30){ // with too many bars the axis label gets too crowded // Hmm actually this isn't toggling back to auto when we have // lots of bars and performance tanks so we better just leave // autoformatting on for now. layout.xaxis.autotick = true; layout.xaxis.autorange = true; layout.xaxis.dtick = ''; layout.xaxis.ticks = ''; } else { layout.xaxis.autotick = false; layout.xaxis.dtick = (maxtime/numbars); } */ let halfpoint; if(logy.checked) { layout.yaxis.type="log" // on log plots the half-way point goofs it up so we have to manually // map the annotation halfpoint = Math.log10(initial * 0.5) } else { layout.yaxis.type="" halfpoint = initial * 0.5 } if(logx.checked) { layout.xaxis.type="log" } else { layout.xaxis.type="" } if (hlnote.checked && halflife<=maxtime) { layout.annotations= [ { x: halflife, y: halfpoint, xref: 'x', yref: 'y', text: 'Half of theatoms remain', showarrow: true, font: { size: 16, }, arrowhead: 7, opacity: 0.8, bgcolor: 'white', ax: 0, ay: -40 } ] } else { layout.annotations=[] } var data=[line, radioactive, decayed ]; Plotly.react('plot', data, layout); } var trace1 = { }; var trace2 = { }; var data = [trace1, trace2]; var layout = {barmode: 'stack', yaxis: { type: 'linear', autorange: true , title: { text: 'Number of atoms', }, }, xaxis: { autotick: true, nticks: 10, title: { text: 'Time (years)', }}, showlegend: true, legend: { x: 1, xanchor: 'right', y: 1, font: { size: 18, }, orientation: "h", bgcolor: 'rgba(255,255,255,0.8)' }, autosize: true, margin: { t: 0 }, }; var config = { 'displayModeBar': false } Plotly.newPlot('plot', data, layout, config); window.onresize = function() { Plotly.relayout('plot', {}) } // compute initial values compute(); </script>