Understanding the dose rate of radiation is crucial for safety in industrial, medical, and scientific environments. The dose rate determines how much radiation energy is absorbed by an object or person per unit of time.
The Point Source Formula
For a point source of gamma radiation, the dose rate follows the Inverse Square Law. The basic physics formula is:
D = (A × Γ) / d²
Where:
D: Dose Rate (typically in mSv/h).
A: Activity of the radioactive source (in Gigabecquerels, GBq).
Γ (Gamma): The specific gamma-ray constant for the isotope (mSv·m² / h·GBq).
d: Distance from the source (in meters).
Common Specific Gamma-Ray Constants
Isotope
Gamma Constant (mSv·m²/h·GBq)
Half-Life
Cobalt-60
0.306
5.27 years
Cesium-137
0.077
30.17 years
Iridium-192
0.138
73.8 days
Practical Example
Imagine you are working with a Cobalt-60 source with an activity of 100 GBq. You are standing 5 meters away from the source. What is your hourly dose rate?
Radiation safety relies on the ALARA principle: As Low As Reasonably Achievable. The three main pillars of protection are:
Time: Minimize the time spent near a source.
Distance: Increase distance (doubling the distance reduces the dose rate to one-fourth).
Shielding: Use appropriate materials (like lead or concrete) to absorb radiation.
Note: This calculator is for educational purposes and provides estimates for point sources in a vacuum/air without shielding. Real-world scenarios involving scattering and shielding require complex professional modeling.
function updateGamma() {
var isotopeSelect = document.getElementById("isotope");
var customDiv = document.getElementById("customGammaDiv");
var gammaInput = document.getElementById("gammaConstant");
if (isotopeSelect.value === "custom") {
customDiv.style.display = "block";
} else {
customDiv.style.display = "none";
gammaInput.value = isotopeSelect.value;
}
}
function calculateDoseRate() {
var gamma = parseFloat(document.getElementById("gammaConstant").value);
var activity = parseFloat(document.getElementById("activity").value);
var distance = parseFloat(document.getElementById("distance").value);
var resultDiv = document.getElementById("radResult");
var doseRateDisplay = document.getElementById("doseRateVal");
var safetyNote = document.getElementById("safetyNote");
if (isNaN(gamma) || isNaN(activity) || isNaN(distance) || distance <= 0 || activity <= 0) {
alert("Please enter valid positive numbers for Activity, Distance, and Gamma Constant.");
return;
}
// Formula: D = (A * Gamma) / d^2
var doseRate = (activity * gamma) / (distance * distance);
resultDiv.style.display = "block";
// Formatting result
if (doseRate 100) {
safetyNote.innerHTML = "Warning: Extremely high radiation field. Immediate shielding and evacuation protocols required.";
safetyNote.style.color = "#c0392b";
} else if (doseRate > 0.02) {
safetyNote.innerHTML = "Caution: This dose rate exceeds standard public hourly limits. Professional monitoring required.";
safetyNote.style.color = "#d35400";
} else {
safetyNote.innerHTML = "Note: Always monitor dose levels with a calibrated dosimeter.";
safetyNote.style.color = "#666";
}
// Smooth scroll to result
resultDiv.scrollIntoView({ behavior: 'smooth', block: 'nearest' });
}