Radioactive Decay Rate Calculator
Understanding radioactive decay is fundamental in nuclear physics and chemistry. Radioactive decay is the process by which an unstable atomic nucleus loses energy by emitting radiation. This process is characterized by a decay rate, which quantifies how quickly a sample of a radioactive substance diminishes over time. The decay rate is often expressed in terms of the decay constant (λ), which represents the probability of a single nucleus decaying per unit time. The half-life (t½) of a radioactive isotope is the time it takes for half of the radioactive atoms in a sample to decay. These two quantities are inversely related and are crucial for determining the age of materials (radiometric dating) or assessing radiation exposure.
function calculateDecayRate() {
var initialAmount = parseFloat(document.getElementById("initialAmount").value);
var finalAmount = parseFloat(document.getElementById("finalAmount").value);
var timeElapsed = parseFloat(document.getElementById("timeElapsed").value);
var resultDiv = document.getElementById("result");
var decayConstantResultDiv = document.getElementById("decayConstantResult");
var halfLifeResultDiv = document.getElementById("halfLifeResult");
resultDiv.innerHTML = "";
decayConstantResultDiv.innerHTML = "";
halfLifeResultDiv.innerHTML = "";
if (isNaN(initialAmount) || isNaN(finalAmount) || isNaN(timeElapsed)) {
resultDiv.innerHTML = "Please enter valid numbers for all fields.";
return;
}
if (initialAmount <= 0 || finalAmount < 0 || timeElapsed initialAmount) {
resultDiv.innerHTML = "Final amount cannot be greater than the initial amount.";
return;
}
// Calculate the decay rate (average rate of decrease)
var decayRate = (initialAmount – finalAmount) / timeElapsed;
resultDiv.innerHTML = "Average Decay Rate: " + decayRate.toFixed(6) + " per unit of time";
// Calculate the decay constant (λ) using the formula: N(t) = N0 * e^(-λt)
// Rearranging gives: λ = -ln(N(t)/N0) / t
// Using N(t) = finalAmount, N0 = initialAmount, t = timeElapsed
if (finalAmount > 0) {
var decayConstant = -Math.log(finalAmount / initialAmount) / timeElapsed;
decayConstantResultDiv.innerHTML = "Decay Constant (λ): " + decayConstant.toExponential(4) + " per unit of time";
// Calculate the half-life (t½) using the formula: t½ = ln(2) / λ
var halfLife = Math.log(2) / decayConstant;
halfLifeResultDiv.innerHTML = "Half-Life (t½): " + halfLife.toFixed(2) + " units of time";
} else {
// If finalAmount is 0, it implies infinite half-life or it has completely decayed.
// For practical purposes and to avoid division by zero in half-life calculation,
// we can state it has fully decayed or half-life is effectively infinite for
// calculations involving decay constant.
decayConstantResultDiv.innerHTML = "Decay Constant (λ): The sample has completely decayed.";
halfLifeResultDiv.innerHTML = "Half-Life (t½): The sample has completely decayed.";
}
}
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font-family: sans-serif;
max-width: 600px;
margin: 20px auto;
padding: 20px;
border: 1px solid #ccc;
border-radius: 8px;
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.input-group input[type="number"] {
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}
#result, #decayConstantResult, #halfLifeResult {
margin-bottom: 10px;
color: #333;
font-size: 1.1em;
}