Calculate Decay Rate from Half Life

Half-Life to Decay Rate Calculator

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function calculateDecayRate() { var halfLife = parseFloat(document.getElementById("halfLife").value); var timeUnits = document.getElementById("timeUnits").value; var resultDiv = document.getElementById("result"); if (isNaN(halfLife) || halfLife <= 0) { resultDiv.innerHTML = "Please enter a valid positive number for Half-Life."; return; } // The formula to convert half-life (t_1/2) to decay constant (lambda) is: // lambda = ln(2) / t_1/2 // where ln(2) is the natural logarithm of 2, approximately 0.693. var decayRate = Math.log(2) / halfLife; // Using Math.log for natural logarithm var explanation = "Explanation:"; explanation += "The half-life (t1/2) of a substance is the time it takes for half of the radioactive atoms in a sample to decay."; explanation += "The decay rate, also known as the decay constant (λ), is a measure of how quickly a radioactive substance decays."; explanation += "It represents the probability per unit time that a single atom will decay. The relationship between the decay constant and half-life is given by the formula:"; explanation += "λ = ln(2) / t1/2"; explanation += "Where ln(2) is the natural logarithm of 2 (approximately 0.693). A higher decay constant means a shorter half-life and a faster decay rate."; explanation += "The time units for the decay rate will be the inverse of the units chosen for the half-life (e.g., if half-life is in years, the decay rate will be in per year)."; explanation += ""; var resultHtml = "

Results:

"; resultHtml += "With a half-life of " + halfLife + " " + timeUnits + ":"; resultHtml += "The decay rate (λ) is approximately " + decayRate.toFixed(6) + " per " + timeUnits + "."; resultHtml += explanation; resultDiv.innerHTML = resultHtml; } .calculator-wrapper { font-family: Arial, sans-serif; border: 1px solid #ccc; padding: 20px; border-radius: 8px; max-width: 500px; margin: 20px auto; background-color: #f9f9f9; } .calculator-wrapper h2 { text-align: center; margin-bottom: 20px; color: #333; } .input-group { margin-bottom: 15px; display: flex; flex-direction: column; } .input-group label { margin-bottom: 5px; font-weight: bold; color: #555; } .input-group input[type="number"], .input-group select { padding: 10px; border: 1px solid #ccc; border-radius: 4px; font-size: 1em; } .calculator-wrapper button { background-color: #007bff; color: white; padding: 12px 20px; border: none; border-radius: 4px; cursor: pointer; font-size: 1.1em; width: 100%; transition: background-color 0.3s ease; } .calculator-wrapper button:hover { background-color: #0056b3; } #result { margin-top: 25px; padding-top: 15px; border-top: 1px dashed #eee; } #result h3 { margin-bottom: 10px; color: #333; } #result p { line-height: 1.6; color: #444; } #result strong { color: #007bff; } code { background-color: #e9e9e9; padding: 2px 5px; border-radius: 3px; font-family: Consolas, Monaco, 'Andale Mono', 'Ubuntu Mono', monospace; }

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