Radioactive Activity Calculator

Initial Activity (Becquerels, Bq):

Half-Life (seconds):

Time Elapsed (seconds):

function calculateActivity() { var initialActivityInput = document.getElementById("initialActivity"); var halfLifeInput = document.getElementById("halfLife"); var timeElapsedInput = document.getElementById("timeElapsed"); var resultDiv = document.getElementById("result"); var initialActivity = parseFloat(initialActivityInput.value); var halfLife = parseFloat(halfLifeInput.value); var timeElapsed = parseFloat(timeElapsedInput.value); if (isNaN(initialActivity) || isNaN(halfLife) || isNaN(timeElapsed) || initialActivity <= 0 || halfLife <= 0 || timeElapsed < 0) { resultDiv.innerHTML = "Please enter valid positive numbers for Initial Activity and Half-Life, and a non-negative number for Time Elapsed."; return; } // Formula for radioactive decay: A(t) = A0 * (1/2)^(t / T_half) // Where: // A(t) is the activity at time t // A0 is the initial activity // t is the time elapsed // T_half is the half-life var exponent = timeElapsed / halfLife; var decayFactor = Math.pow(0.5, exponent); var finalActivity = initialActivity * decayFactor; resultDiv.innerHTML = "

Result:

The remaining activity after " + timeElapsed + " seconds is " + finalActivity.toLocaleString('en-US', { maximumFractionDigits: 2 }) + " Becquerels (Bq)."; }

Understanding Radioactive Activity and Decay

Radioactive activity is a measure of the rate at which a radioactive substance undergoes decay. It quantifies how many atomic nuclei in a sample disintegrate per unit of time. The standard unit for radioactive activity is the Becquerel (Bq), which is defined as one decay per second. Another common unit, though less used in precise scientific contexts now, is the Curie (Ci).

The Law of Radioactive Decay

Radioactive decay is a spontaneous and random process. However, for a large number of radioactive atoms, the rate of decay follows a predictable pattern described by the law of radioactive decay. This law states that the rate of decay is directly proportional to the number of radioactive nuclei present in the sample.

The activity of a radioactive sample decreases over time as its unstable nuclei transform into more stable forms. This decrease is exponential and is characterized by the half-life of the isotope.

Half-Life

The half-life (often denoted as T_½ or t_½) is the time required for half of the radioactive atoms in a given sample to undergo decay. Each radioactive isotope has a unique and constant half-life, which can range from fractions of a second to billions of years. For example:

Carbon-14 has a half-life of approximately 5,730 years.
Iodine-131 has a half-life of about 8 days.
Uranium-238 has a half-life of about 4.5 billion years.

Calculating Remaining Activity

The activity of a radioactive sample at any given time t can be calculated using the following formula:

A(t) = A₀ × (1/2)^{(t / T_½)}

Where:

A(t) is the activity at time t.
A₀ is the initial activity of the sample.
t is the time elapsed since the initial measurement.
T_½ is the half-life of the radioactive isotope.

This formula shows that after one half-life, the activity will be halved; after two half-lives, it will be reduced to one-quarter of the initial activity, and so on.

Applications

Understanding radioactive decay and activity is crucial in various fields, including:

Nuclear Medicine: Used for diagnosis (e.g., PET scans) and treatment (radiotherapy).
Archaeology: Radiocarbon dating (using Carbon-14) to determine the age of ancient artifacts.
Geology: Dating rocks and geological formations.
Industrial Safety: Monitoring radiation levels and managing radioactive waste.

Example Calculation

Let's say we have a sample of a radioactive isotope with an initial activity of 1,000,000 Becquerels (Bq). This isotope has a half-life of 1,200 seconds (20 minutes). We want to find out the remaining activity after 3,600 seconds (1 hour).

Initial Activity (A₀) = 1,000,000 Bq
Half-Life (T_½) = 1,200 seconds
Time Elapsed (t) = 3,600 seconds

Using the formula:

A(t) = 1,000,000 Bq × (1/2)^{(3600 seconds / 1200 seconds)}

A(t) = 1,000,000 Bq × (1/2)³

A(t) = 1,000,000 Bq × (1/8)

A(t) = 125,000 Bq

Therefore, after 1 hour, the radioactive activity of the sample will be reduced to 125,000 Becquerels.