Nuclear equations describe the transformations that occur during nuclear reactions, such as radioactive decay and nuclear fission. Unlike chemical equations where atoms are rearranged, nuclear equations represent changes to the nucleus of an atom, often resulting in the formation of different elements.
Conservation Laws in Nuclear Reactions
The fundamental principle guiding nuclear equations is the conservation of mass-energy and charge. This means:
Conservation of Mass Number (A): The total number of protons and neutrons (the mass number) must be the same on both sides of the equation.
Conservation of Atomic Number (Z): The total number of protons (the atomic number, which defines the element) must be the same on both sides of the equation.
Notation for Nuclides
Nuclides (specific types of atomic nuclei) are typically represented using the following notation: AZX, where:
X is the chemical symbol of the element.
A is the mass number (number of protons + neutrons).
Z is the atomic number (number of protons).
For example, a Uranium-235 nucleus is written as 23592U.
Common Nuclear Particles
Here are some common particles involved in nuclear reactions:
Alpha particle (α): A helium nucleus, 42He.
Beta particle (β–): An electron emitted during beta decay, 0-1e.
Positron (β+): An antiparticle of an electron emitted during positron emission, 0+1e.
Gamma ray (γ): A high-energy photon, often represented as 00γ, as it has no mass or charge.
Neutron (n):10n.
Proton (p):11p.
How to Use This Calculator
This calculator helps to verify if a given nuclear equation is balanced based on the conservation of mass number and atomic number. It's particularly useful for identifying missing reactants or products, or confirming the validity of a proposed reaction.
Enter Reactants: Input the mass number and atomic number for each reactant (e.g., 235U for Uranium-235, or 4He for an alpha particle). If there's only one reactant (like in alpha or beta decay), only fill the first reactant field.
Enter Products: Input the mass number and atomic number for each product.
Click "Balance Equation": The calculator will sum the mass numbers and atomic numbers on both sides.
Note: For particles like neutrons or alpha particles, you can directly input their common symbols (e.g., 1n, 4He). The calculator will parse these. For elements, you must provide the mass number and element symbol (e.g., 235U, 141Ba).
Example: Nuclear Fission of Uranium-235
A common nuclear fission reaction is:
23592U + 10n → 14156Ba + 9236Kr + 3 10n
To use the calculator for this example:
Reactant 1: 235U
Reactant 2: 1n
Product 1: 141Ba
Product 2: 92Kr
Product 3: 3 1n
The calculator will then check if:
Reactant Mass Sum (235 + 1) = Product Mass Sum (141 + 92 + 3*1)
Reactant Atomic Sum (92 + 0) = Product Atomic Sum (56 + 36 + 3*0)
In this case, both sums are equal, confirming the equation is balanced.
// Function to parse mass number and atomic number from input string
function parseNuclide(nuclideStr) {
nuclideStr = nuclideStr.trim();
var massNum = 0;
var atomicNum = 0;
var elementSymbol = "";
var coefficient = 1;
// Handle coefficients like "3 1n"
var coefficientMatch = nuclideStr.match(/^(\d+)\s+(.*)/);
if (coefficientMatch) {
coefficient = parseInt(coefficientMatch[1], 10);
nuclideStr = coefficientMatch[2].trim();
}
// Common particle abbreviations
if (nuclideStr.toLowerCase() === '1n' || nuclideStr.toLowerCase() === 'n') {
return { mass: 1 * coefficient, atomic: 0, symbol: 'n' };
} else if (nuclideStr.toLowerCase() === '4he' || nuclideStr.toLowerCase() === 'α') {
return { mass: 4 * coefficient, atomic: 2, symbol: 'He' };
} else if (nuclideStr.toLowerCase() === '0e' || nuclideStr.toLowerCase() === 'β-') {
return { mass: 0 * coefficient, atomic: -1, symbol: 'e' };
} else if (nuclideStr.toLowerCase() === 'γ') {
return { mass: 0 * coefficient, atomic: 0, symbol: 'γ' };
}
// General format: A Z X or just A X or just X
var match = nuclideStr.match(/^(?:(\d+))?([A-Za-z]+)$/); // Matches A X or X
if (match) {
elementSymbol = match[2];
if (match[1]) {
massNum = parseInt(match[1], 10);
} else {
// If no mass number is given, try to find atomic number from element symbol
// This is a simplification; a full periodic table lookup would be more robust
var atomicMap = {
'H': 1, 'He': 2, 'Li': 3, 'Be': 4, 'B': 5, 'C': 6, 'N': 7, 'O': 8, 'F': 9, 'Ne': 10,
'Na': 11, 'Mg': 12, 'Al': 13, 'Si': 14, 'P': 15, 'S': 16, 'Cl': 17, 'Ar': 18,
'K': 19, 'Ca': 20, 'Sc': 21, 'Ti': 22, 'V': 23, 'Cr': 24, 'Mn': 25, 'Fe': 26, 'Co': 27, 'Ni': 28, 'Cu': 29, 'Zn': 30,
'Ga': 31, 'Ge': 32, 'As': 33, 'Se': 34, 'Br': 35, 'Kr': 36, 'Rb': 37, 'Sr': 38, 'Y': 39, 'Zr': 40,
'Nb': 41, 'Mo': 42, 'Tc': 43, 'Ru': 44, 'Rh': 45, 'Pd': 46, 'Ag': 47, 'Cd': 48, 'In': 49, 'Sn': 50,
'Sb': 51, 'Te': 52, 'I': 53, 'Xe': 54, 'Cs': 55, 'Ba': 56, 'La': 57, 'Ce': 58, 'Pr': 59, 'Nd': 60, 'Pm': 61, 'Sm': 62, 'Eu': 63, 'Gd': 64, 'Tb': 65, 'Dy': 66, 'Ho': 67, 'Er': 68, 'Tm': 69, 'Yb': 70, 'Lu': 71, 'Hf': 72, 'Ta': 73, 'W': 74, 'Re': 75, 'Os': 76, 'Ir': 77, 'Pt': 78, 'Au': 79, 'Hg': 80,
'Tl': 81, 'Pb': 82, 'Bi': 83, 'Po': 84, 'At': 85, 'Rn': 86, 'Fr': 87, 'Ra': 88, 'Ac': 89, 'Th': 90, 'Pa': 91, 'U': 92, 'Np': 93, 'Pu': 94, 'Am': 95, 'Cm': 96, 'Bk': 97, 'Cf': 98, 'Es': 99, 'Fm': 100, 'Md': 101, 'No': 102, 'Lr': 103, 'Rf': 104, 'Db': 105, 'Sg': 106, 'Bh': 107, 'Hs': 108, 'Mt': 109, 'Ds': 110, 'Rg': 111, 'Cn': 112, 'Nh': 113, 'Fl': 114, 'Mc': 115, 'Lv': 116, 'Ts': 117, 'Og': 118
};
atomicNum = atomicMap[elementSymbol] || 0; // Default to 0 if symbol not found
}
} else {
var fullMatch = nuclideStr.match(/^(\d+)(\d+)([A-Za-z]+)$/); // Matches A Z X
if (fullMatch) {
massNum = parseInt(fullMatch[1], 10);
atomicNum = parseInt(fullMatch[2], 10);
elementSymbol = fullMatch[3];
}
}
return { mass: massNum * coefficient, atomic: atomicNum * coefficient, symbol: elementSymbol };
}
function calculateNuclearEquation() {
var resultDiv = document.getElementById('result');
resultDiv.innerHTML = "; // Clear previous results
var r1Str = document.getElementById('reactant1').value;
var r2Str = document.getElementById('reactant2').value;
var p1Str = document.getElementById('product1').value;
var p2Str = document.getElementById('product2').value;
var p3Str = document.getElementById('product3').value;
var reactants = [];
if (r1Str) reactants.push(parseNuclide(r1Str));
if (r2Str) reactants.push(parseNuclide(r2Str));
var products = [];
if (p1Str) products.push(parseNuclide(p1Str));
if (p2Str) products.push(parseNuclide(p2Str));
if (p3Str) products.push(parseNuclide(p3Str));
if (reactants.length === 0 || products.length === 0) {
resultDiv.innerHTML = 'Error: Please enter at least one reactant and one product.';
return;
}
var totalReactantMass = 0;
var totalReactantAtomic = 0;
for (var i = 0; i < reactants.length; i++) {
if (isNaN(reactants[i].mass) || isNaN(reactants[i].atomic)) {
resultDiv.innerHTML = 'Error: Invalid input in reactants.';
return;
}
totalReactantMass += reactants[i].mass;
totalReactantAtomic += reactants[i].atomic;
}
var totalProductMass = 0;
var totalProductAtomic = 0;
for (var i = 0; i < products.length; i++) {
if (isNaN(products[i].mass) || isNaN(products[i].atomic)) {
resultDiv.innerHTML = 'Error: Invalid input in products.';
return;
}
totalProductMass += products[i].mass;
totalProductAtomic += products[i].atomic;
}
var massBalanced = totalReactantMass === totalProductMass;
var atomicBalanced = totalReactantAtomic === totalProductAtomic;
var message = "";
if (massBalanced && atomicBalanced) {
message = "Equation is BALANCED.";
resultDiv.style.backgroundColor = '#d4edda'; // Success Green background
resultDiv.style.color = '#155724'; // Darker green text
resultDiv.style.borderColor = '#c3e6cb';
} else {
message = "Equation is NOT BALANCED.";
resultDiv.style.backgroundColor = '#f8d7da'; // Error Red background
resultDiv.style.color = '#721c24'; // Darker red text
resultDiv.style.borderColor = '#f5c6cb';
}
resultDiv.innerHTML = message +
`Reactants: Mass=${totalReactantMass}, Atomic=${totalReactantAtomic}` +
`Products: Mass=${totalProductMass}, Atomic=${totalProductAtomic}`;
}