Understanding Rate of Decay
The rate of decay describes how a quantity decreases over a specific period. In many scientific contexts, this is related to concepts like radioactive decay, where unstable atomic nuclei lose energy by emitting radiation. The decay rate can be calculated using the following formula:
Decay Rate = ((Initial Quantity – Final Quantity) / Initial Quantity) / Time Elapsed
A positive rate indicates decay, while a negative rate would imply growth. For instance, if you start with 100 grams of a substance and after 10 hours you have 75 grams remaining, the decay rate helps quantify how fast that loss occurred.
Example: Suppose you have 100 grams of a radioactive isotope. After 2 hours, only 80 grams remain.
Initial Quantity = 100g
Final Quantity = 80g
Time Elapsed = 2 hours
The reduction in quantity is 100g – 80g = 20g.
The fraction of decay is 20g / 100g = 0.2.
The rate of decay per hour is 0.2 / 2 hours = 0.1 per hour, or 10% per hour.
function calculateRateOfDecay() {
var initialQuantity = parseFloat(document.getElementById("initialQuantity").value);
var finalQuantity = parseFloat(document.getElementById("finalQuantity").value);
var timeElapsed = parseFloat(document.getElementById("timeElapsed").value);
var resultDiv = document.getElementById("result");
resultDiv.innerHTML = ""; // Clear previous results
if (isNaN(initialQuantity) || isNaN(finalQuantity) || isNaN(timeElapsed)) {
resultDiv.innerHTML = "Please enter valid numbers for all fields.";
return;
}
if (initialQuantity <= 0) {
resultDiv.innerHTML = "Initial quantity must be greater than zero.";
return;
}
if (timeElapsed initialQuantity) {
resultDiv.innerHTML = "Final quantity cannot be greater than the initial quantity for decay.";
return;
}
var quantityLost = initialQuantity – finalQuantity;
var fractionalDecay = quantityLost / initialQuantity;
var rateOfDecay = fractionalDecay / timeElapsed;
resultDiv.innerHTML = "
Rate of Decay: " + rateOfDecay.toFixed(4) + " per unit of time";
resultDiv.innerHTML += "
(This represents a " + (rateOfDecay * 100).toFixed(2) + "% decrease per unit of time)";
}
.calculator-wrapper {
font-family: Arial, sans-serif;
display: flex;
flex-wrap: wrap;
gap: 20px;
max-width: 900px;
margin: 20px auto;
padding: 20px;
border: 1px solid #ddd;
border-radius: 8px;
background-color: #f9f9f9;
}
.calculator-form {
flex: 1;
min-width: 300px;
background-color: #fff;
padding: 20px;
border-radius: 8px;
box-shadow: 0 2px 4px rgba(0,0,0,0.1);
}
.calculator-form h2 {
margin-top: 0;
color: #333;
}
.form-group {
margin-bottom: 15px;
}
.form-group label {
display: block;
margin-bottom: 5px;
font-weight: bold;
color: #555;
}
.form-group input[type="number"] {
width: calc(100% – 22px);
padding: 10px;
border: 1px solid #ccc;
border-radius: 4px;
box-sizing: border-box;
}
.calculator-form button {
background-color: #4CAF50;
color: white;
padding: 10px 15px;
border: none;
border-radius: 4px;
cursor: pointer;
font-size: 16px;
transition: background-color 0.3s ease;
}
.calculator-form button:hover {
background-color: #45a049;
}
.result-display {
margin-top: 20px;
padding: 15px;
border: 1px solid #e0e0e0;
border-radius: 4px;
background-color: #f0f0f0;
min-height: 50px;
color: #333;
}
.calculator-explanation {
flex: 1;
min-width: 300px;
background-color: #e7f3fe;
padding: 20px;
border-radius: 8px;
box-shadow: 0 2px 4px rgba(0,0,0,0.05);
}
.calculator-explanation h3 {
margin-top: 0;
color: #2c3e50;
}
.calculator-explanation p {
line-height: 1.6;
color: #444;
}
.calculator-explanation strong {
color: #34495e;
}