Calculate Density from Atomic Radius and Atomic Weight
Calculate Density
Enter the atomic radius of the element in picometers (pm).
Enter the atomic weight of the element in atomic mass units (amu).
Enter the packing efficiency (a decimal between 0 and 1). Common values: 0.74 (FCC, HCP), 0.68 (BCC), 0.52 (SC).
Avogadro's constant (mol⁻¹). Typically fixed.
Calculation Results
—
—Volume (V)
—Molar Mass (kg/mol)
—Atoms per Unit Cell (n)
Formula Used: Density (ρ) = (n * M) / (V * N_A)
Where:
ρ = Density
n = Atoms per unit cell (calculated from Packing Efficiency and Unit Cell Volume)
M = Molar Mass (converted to kg/mol)
V = Volume of the unit cell (derived from atomic radius)
N_A = Avogadro's Constant
Density vs. Atomic Radius
Illustrating how density changes with atomic radius for a fixed atomic weight and packing efficiency.
What is Density Calculation from Atomic Radius and Atomic Weight?
The calculation of density from atomic radius and atomic weight is a fundamental concept in materials science and solid-state physics. It allows us to predict or understand the mass per unit volume of a crystalline solid by leveraging the properties of its constituent atoms. This method is crucial for characterizing new materials, understanding their structural properties, and predicting their behavior under various conditions. It bridges the microscopic world of atoms with the macroscopic observable property of density.
Who Should Use It?
This calculation is particularly relevant for:
Materials Scientists: To characterize and compare different crystalline structures and alloys.
Solid-State Physicists: To study the relationship between atomic structure and bulk properties.
Chemical Engineers: In designing processes where material density is a critical parameter.
Students and Educators: For learning and teaching fundamental principles of crystallography and material properties.
Common Misconceptions
A common misconception is that atomic radius directly dictates density. While a larger atomic radius might intuitively suggest lower density (more space between atoms), the arrangement of these atoms (packing efficiency) and their individual mass (atomic weight) play equally significant roles. Another misconception is that all elements pack their atoms in the same way; in reality, different crystal structures (like FCC, BCC, HCP) have distinct packing efficiencies, dramatically influencing the overall density. Furthermore, assuming a constant packing efficiency for all calculations without considering the specific crystal structure is often inaccurate.
Density Calculation Formula and Mathematical Explanation
The density of a crystalline material can be precisely calculated using its atomic radius, atomic weight, and packing efficiency. The core idea is to determine the mass within a representative volume, typically a unit cell.
Step-by-Step Derivation
1. Calculate the Volume of the Unit Cell (V): For simplicity, we often assume a cubic unit cell where the edge length 'a' is related to the atomic radius 'r'. A common approximation, especially for close-packed structures or BCC, is that the atoms touch along the face diagonal or body diagonal. For a simple cubic (SC) structure, a = 2r. For body-centered cubic (BCC), atoms touch along the body diagonal, so sqrt(3)a = 4r, meaning a = 4r/sqrt(3). For face-centered cubic (FCC) and hexagonal close-packed (HCP), atoms touch along the face diagonal, so sqrt(2)a = 4r, meaning a = 4r/sqrt(2) = 2*sqrt(2)*r. The volume of the unit cell is then V = a³. For this calculator, we use a more general approach by calculating the effective volume occupied by atoms based on packing efficiency. The volume of a single atom (approximated as a sphere) is (4/3)πr³. The total volume occupied by 'n' atoms in a unit cell, considering packing efficiency η, is V_total = n * (Volume of one atom) / η. However, a more direct way to calculate the unit cell volume 'a³' given 'r' depends on the crystal structure. For many common structures (FCC, HCP, BCC), 'a' can be related to 'r'. A simplified approach used here relates the volume 'V' occupied by atoms to their radius and packing efficiency, assuming V is proportional to (2r)³ which is the bounding box volume, then adjusted by packing efficiency.
2. Determine the Number of Atoms per Unit Cell (n): This is determined by the crystal structure's packing efficiency (η). The packing efficiency is defined as the ratio of the volume occupied by atoms to the total volume of the unit cell: η = (n * Volume of one atom) / V_unit_cell. The calculator infers 'n' from the given packing efficiency and the volume derived from the atomic radius.
3. Convert Atomic Weight (M) to Molar Mass in kg/mol: The atomic weight is usually given in atomic mass units (amu). We convert this to kg/mol by multiplying by the conversion factor (approximately 1 kg/mol = 1 amu * N_A). More practically, we can use M (in amu) directly and convert the final density unit.
4. Calculate Mass within the Unit Cell: The total mass in the unit cell is (n * M) / N_A, where M is the molar mass in g/mol and N_A is Avogadro's number. If M is in amu, the mass of 'n' atoms is simply n * M (in amu).
5. Calculate Density (ρ): Density is mass per unit volume. ρ = Mass / Volume. Using SI units: ρ (kg/m³) = (n * M_molar_kg) / V_unit_cell_m³. Using the provided calculator inputs, we calculate the effective volume V based on radius and packing efficiency, convert Molar Weight M to kg/mol, and use the formula derived from the definition of packing efficiency.
Simplified Formula Used by Calculator:
The calculator uses a derived relationship. First, the volume of a single atom is approximated as $V_{atom} = \frac{4}{3}\pi r^3$. The total volume of the unit cell $V_{cell}$ can be related to this atomic volume and the packing efficiency $\eta$: $V_{cell} = \frac{n \times V_{atom}}{\eta}$. This step is complex as 'n' depends on the structure type. A more practical approach for the calculator is to estimate the unit cell edge 'a' based on 'r' and the packing efficiency, and then calculate $V_{cell} = a^3$. For example, for FCC/HCP, $a \approx 2\sqrt{2}r$, so $V_{cell} \approx (2\sqrt{2}r)^3 = 16\sqrt{2}r^3$. For BCC, $a \approx \frac{4r}{\sqrt{3}}$, so $V_{cell} \approx (\frac{4r}{\sqrt{3}})^3 = \frac{64r^3}{3\sqrt{3}}$. The calculator uses a general approximation for volume derived from radius and packing efficiency.
The mass of the atoms in the unit cell is $Mass_{cell} = n \times \frac{M}{N_A}$ (where M is molar mass in g/mol, resulting mass in grams). To get density in kg/m³:
Density $ \rho = \frac{n \times M \text{ (in kg/mol)}}{V_{cell} \text{ (in m}^3 \text{)} \times N_A}$
The calculator rearranges this using the packing efficiency definition $ V_{cell} = \frac{n \times (\frac{4}{3}\pi r^3)}{\eta} $ (assuming r is in meters):
$ \rho = \frac{n \times M \text{ (in kg/mol)}}{(\frac{n \times (\frac{4}{3}\pi r^3)}{\eta}) \times N_A} = \frac{M \text{ (in kg/mol)} \times \eta}{N_A \times \frac{4}{3}\pi r^3}$
This simplifies to Density = (Molar Mass * Packing Efficiency) / (Avogadro's Number * Volume of one atom), where units must be consistent (e.g., r in meters, M in kg/mol).
Aluminum is a common metal known for its low density and good corrosion resistance. It crystallizes in a face-centered cubic (FCC) structure.
Inputs:
Atomic Radius (r) of Al ≈ 143 pm
Atomic Weight (M) of Al ≈ 26.98 amu
Packing Efficiency (η) for FCC ≈ 0.74
Avogadro's Constant (NA) = 6.022 x 1023 mol-1
Calculation Steps:
Convert atomic radius to meters: r = 143 pm = 143 x 10⁻¹² m.
Calculate the volume of one atom: $V_{atom} = \frac{4}{3}\pi (143 \times 10^{-12} \text{ m})^3 \approx 1.22 \times 10^{-35} \text{ m}^3$.
Estimate the unit cell volume (V_cell): Using the FCC formula $V_{cell} \approx 16\sqrt{2}r^3 \approx 16\sqrt{2}(143 \times 10^{-12})^3 \approx 1.95 \times 10^{-29} \text{ m}^3$. Alternatively, using packing efficiency: $V_{cell} = \frac{n \times V_{atom}}{\eta}$. For FCC, n=4. $V_{cell} = \frac{4 \times 1.22 \times 10^{-35} \text{ m}^3}{0.74} \approx 1.65 \times 10^{-35} \text{ m}^3$. There's a discrepancy due to approximations. Let's use the calculator's method which directly relates them.
Convert atomic weight to kg/mol: M = 26.98 amu ≈ 0.02698 kg/mol.
Result: The calculated density is approximately 2717 kg/m³. This is very close to the actual density of Aluminum, which is around 2700 kg/m³.
Interpretation: This confirms that Aluminum is a relatively lightweight metal, suitable for applications where weight reduction is important, such as in aerospace and automotive industries.
How to Use This Density Calculator
Our online density calculator is designed for ease of use. Follow these simple steps to get accurate results:
Input Atomic Radius: Enter the atomic radius of the element in picometers (pm) into the 'Atomic Radius (r)' field.
Input Atomic Weight: Enter the atomic weight of the element in atomic mass units (amu) into the 'Atomic Weight (M)' field.
Input Packing Efficiency: Enter the packing efficiency (η) as a decimal value (e.g., 0.74 for FCC/HCP structures). Refer to the helper text for common values.
Avogadro's Constant: This value is pre-filled as it's a physical constant.
Click Calculate: Press the 'Calculate Density' button.
How to Read Results
Upon clicking 'Calculate', the calculator will display:
Primary Result: The calculated density, shown prominently in g/cm³ (grams per cubic centimeter), a common unit for material density.
Intermediate Values:
Volume (V): The calculated volume of the unit cell in cubic meters (m³).
Molar Mass (kg/mol): The atomic weight converted to kilograms per mole (kg/mol).
Atoms per Unit Cell (n): An inferred number of atoms based on packing efficiency and typical crystal structures.
Formula Explanation: A clear breakdown of the mathematical formula used.
Decision-Making Guidance
Use the calculated density to:
Compare different materials for specific applications (e.g., choosing a lightweight metal for an aircraft).
Verify experimental measurements.
Understand the relationship between atomic properties and bulk material characteristics.
If the calculated density seems unusually high or low, double-check your input values, especially the atomic radius and packing efficiency, as these can vary depending on the source and specific conditions.
Key Factors That Affect Density Results
Several factors influence the accuracy and interpretation of density calculations derived from atomic properties. Understanding these is key to reliable material analysis:
Atomic Radius Variations: Atomic radius is not a fixed value. It can change slightly depending on the bonding environment, coordination number, and oxidation state of the atom. Different sources may provide slightly different values, affecting the final density calculation. This is a fundamental aspect affecting the precision of any calculation based on atomic radius.
Crystal Structure and Packing Efficiency (η): The way atoms are arranged in a solid (its crystal structure) significantly impacts density. Different structures (FCC, BCC, HCP, SC, etc.) have characteristic packing efficiencies. Using an incorrect or assumed packing efficiency for a specific element or compound will lead to inaccurate density results. For example, the density difference between BCC and FCC iron is substantial due to their differing packing efficiencies.
Real Density vs. Theoretical Density: The calculated density is a *theoretical* density based on ideal crystal structures. Real materials often contain defects (vacancies, interstitials, dislocations), impurities, and grain boundaries. These imperfections typically reduce the actual measured density compared to the theoretical value. This is especially true for alloys and non-stoichiometric compounds.
Temperature and Pressure: Like most materials, solids expand when heated and contract when cooled. Changes in temperature and pressure affect the interatomic distances and thus the unit cell volume, leading to variations in density. Our calculator assumes standard conditions. For high-precision work, temperature and pressure dependencies must be considered.
Phase Transitions: Many elements and compounds can exist in different crystalline phases (e.g., allotropes of carbon like graphite and diamond). Each phase has a distinct atomic arrangement, packing efficiency, and therefore, density. Ensuring you are using parameters for the correct phase is critical.
Isotopes: While atomic weight is typically an average of naturally occurring isotopes, variations in isotopic composition can lead to minor differences in atomic mass and, consequently, density. This is usually a negligible effect for most practical applications but can be relevant in specialized fields like nuclear physics.
Bonding Type and Interatomic Forces: The nature of chemical bonding (ionic, covalent, metallic) influences the effective size of atoms and the forces holding them together, indirectly affecting atomic radius and packing. Metallic bonds typically allow for closer packing than strongly directional covalent bonds.
Frequently Asked Questions (FAQ)
What is the difference between atomic weight and molar mass?
Atomic weight is the mass of a single atom relative to 1/12th the mass of a carbon-12 atom, typically expressed in atomic mass units (amu). Molar mass is the mass of one mole of a substance, expressed in grams per mole (g/mol) or kilograms per mole (kg/mol). Numerically, the molar mass in g/mol is equivalent to the atomic weight in amu. For calculations requiring SI units, the atomic weight in amu is converted to kg/mol.
Can this calculator be used for amorphous materials (like glass)?
No, this calculator is specifically designed for crystalline materials where atoms are arranged in a regular, repeating lattice structure. Amorphous materials lack this long-range order, and their density is typically determined through direct measurement or different modeling techniques.
Why is the packing efficiency important?
Packing efficiency determines how tightly the atoms are packed within the unit cell. A higher packing efficiency means atoms occupy a larger fraction of the unit cell volume, resulting in a higher density, assuming atomic mass and radius are constant. It's directly dependent on the crystal structure.
What units should I use for atomic radius?
The calculator expects the atomic radius in picometers (pm). Ensure your input value is converted to picometers before entering it. Common values range from around 30 pm (Hydrogen) to over 250 pm (Cesium).
How accurate is the calculated density?
The accuracy depends on the precision of the input values (atomic radius, atomic weight, packing efficiency) and the assumptions made about the crystal structure. The calculation provides a theoretical density. Real-world density can differ due to defects, temperature, pressure, and impurities.
Can this be used for molecules or compounds?
This calculator is primarily for elements. For compounds, you would need to consider the molecular weight, the crystal structure of the compound (which might differ significantly from elemental structures), and potentially effective atomic radii within the compound's bonds, making the calculation more complex.
What does 'n' (atoms per unit cell) represent?
'n' represents the effective number of atoms within one unit cell. For example, in a Simple Cubic (SC) structure, n=1; in Body-Centered Cubic (BCC), n=2; and in Face-Centered Cubic (FCC), n=4. The calculator infers 'n' based on the provided packing efficiency and typical crystal structures.
How do I find the correct packing efficiency for an element?
You can find the packing efficiency for common crystal structures in materials science textbooks or online resources. For example, FCC and HCP structures have a maximum packing efficiency of about 0.74, while BCC is about 0.68, and Simple Cubic is about 0.52. You need to know or research the common crystal structure of the element at standard conditions.
var atomicRadiusInput = document.getElementById("atomicRadius");
var atomicWeightInput = document.getElementById("atomicWeight");
var packingEfficiencyInput = document.getElementById("packingEfficiency");
var avogadroConstantInput = document.getElementById("avogadroConstant");
var atomicRadiusError = document.getElementById("atomicRadiusError");
var atomicWeightError = document.getElementById("atomicWeightError");
var packingEfficiencyError = document.getElementById("packingEfficiencyError");
var resultsContainer = document.getElementById("resultsContainer");
var primaryResult = document.getElementById("primaryResult");
var volumeResult = document.getElementById("volumeResult");
var molarMassInKg = document.getElementById("molarMassInKg");
var atomsPerUnitCell = document.getElementById("atomsPerUnitCell");
var densityChartInstance = null;
var chartCanvas = document.getElementById('densityChart').getContext('2d');
// Default values
var defaultAtomicRadius = 150; // pm
var defaultAtomicWeight = 55.845; // amu (Iron)
var defaultPackingEfficiency = 0.74; // FCC/HCP
function validateInput(value, errorElement, fieldName, min = null, max = null) {
var errorMessage = "";
if (value === "") {
errorMessage = fieldName + " is required.";
} else {
var numValue = parseFloat(value);
if (isNaN(numValue)) {
errorMessage = fieldName + " must be a valid number.";
} else if (numValue < 0) {
errorMessage = fieldName + " cannot be negative.";
} else if (min !== null && numValue max) {
errorMessage = fieldName + " must be no more than " + max + ".";
}
}
errorElement.textContent = errorMessage;
errorElement.style.display = errorMessage ? 'block' : 'none';
return errorMessage === "";
}
function calculateDensity() {
var r_pm = parseFloat(atomicRadiusInput.value);
var M_amu = parseFloat(atomicWeightInput.value);
var eta = parseFloat(packingEfficiencyInput.value);
var NA = parseFloat(avogadroConstantInput.value);
var isValid = true;
isValid = validateInput(atomicRadiusInput.value, atomicRadiusError, "Atomic Radius", 0) && isValid;
isValid = validateInput(atomicWeightInput.value, atomicWeightError, "Atomic Weight", 0) && isValid;
isValid = validateInput(packingEfficiencyInput.value, packingEfficiencyError, "Packing Efficiency", 0, 1) && isValid;
if (!isValid) {
resultsContainer.style.display = 'none';
return;
}
// — Calculations —
// Constants and Conversions
var pmToM = 1e-12; // picometers to meters
var amuToKg = 1.66053906660e-27; // amu to kg
var amuToG = 1.66053906660e-24; // amu to grams
var kgPerMolToGPerMol = 1000; // kg/mol to g/mol
// Convert inputs to SI or consistent units
var r_m = r_pm * pmToM; // Atomic radius in meters
var M_kg_per_mol = M_amu * amuToKg * NA; // Molar mass in kg/mol
// Calculate volume of a single atom (spherical approximation)
var V_atom_m3 = (4/3) * Math.PI * Math.pow(r_m, 3);
// Calculate the unit cell volume (V_cell) using packing efficiency definition
// V_cell = (n * V_atom) / eta
// We need 'n' to calculate V_cell accurately.
// Let's infer 'n' based on typical packing efficiencies for common structures:
// If eta ~0.74 (FCC/HCP), n=4. If eta ~0.68 (BCC), n=2. If eta ~0.52 (SC), n=1.
// This is an approximation, as eta is often derived from n and V_atom/V_cell.
// For simplicity and calculation continuity, we'll assume a relationship that allows calculation.
// A common approach in simplified models: unit cell edge 'a' is related to 'r'.
// For FCC/HCP: a ≈ 2*sqrt(2)*r => V_cell ≈ (2*sqrt(2)*r)^3 = 16*sqrt(2)*r^3
// For BCC: a ≈ 4r/sqrt(3) => V_cell ≈ (4r/sqrt(3))^3 = 64r^3 / (3*sqrt(3))
// Let's use a generic V_cell calculation derived from radius and packing efficiency.
// It's tricky because packing efficiency itself depends on 'n' and 'r'.
// A more direct approach: Density = (Molar Mass * Packing Efficiency) / (Avogadro's Constant * Volume of one atom)
// Requires M in kg/mol, eta unitless, N_A in mol^-1, V_atom in m^3
// Resulting density will be in kg/m^3
var density_kg_per_m3 = (M_kg_per_mol * eta) / (NA * V_atom_m3);
// Convert density to g/cm³ for easier interpretation
// 1 kg/m³ = 0.001 g/cm³
var density_g_per_cm3 = density_kg_per_m3 * 0.001;
// — Intermediate Calculations for Display —
// Approximate number of atoms per unit cell (this is tricky and structure-dependent)
// We can estimate it IF we assume a known structure or use the calculated V_cell
// Let's assume a V_cell derived from r and eta, and then calculate n.
// V_cell = (n * V_atom) / eta => n = (V_cell * eta) / V_atom
// This circularity needs resolution. Let's use an approximation for V_cell based on radius
// For example, assume unit cell edge 'a' is roughly proportional to 2r (bounding box).
// Let's calculate a generic V_cell which IS NOT (n * V_atom) / eta but derived from typical structures
// A simpler, direct calculation for the calculator might be:
// We have r, M, eta, Na.
// We need V_cell and n to display.
// Let's derive V_cell assuming a structure type implied by eta, or a generic bounding box adjusted by eta.
// A very rough estimate for V_cell based on radius: V_cell ≈ (2 * r_m)^3 * eta? No.
// Let's use the formula for V_cell for FCC/HCP as a reference if eta=0.74, or BCC if eta=0.68.
// This calculator simplifies by directly calculating density.
// For display purposes, let's calculate an *effective* volume and *effective* n.
// Let's re-approach: The formula ρ = (n * M) / (V_cell * N_A) IS the definition.
// Packing fraction η = (n * Volume_atom) / V_cell
// V_cell = (n * (4/3)πr³) / η
// Substituting V_cell into density formula:
// ρ = (n * M) / [ ((n * (4/3)πr³) / η) * N_A ]
// ρ = (M * η) / [ (4/3)πr³ * N_A ]
// This is the formula we used! It directly gives density without needing n or V_cell explicitly.
//
// To display INTERMEDIATE values (V_cell and n), we MUST make assumptions.
// Let's ASSUME typical crystal structure corresponding to the eta input:
var n_atoms = 1; // Default for SC
var V_cell_m3 = Math.pow(2 * r_m, 3); // Default bounding box approx for SC
if (eta >= 0.72) { // Approximate range for FCC/HCP
n_atoms = 4;
// For FCC, a = 2*sqrt(2)*r => V_cell = (2*sqrt(2)*r)^3
V_cell_m3 = Math.pow(2 * Math.SQRT2 * r_m, 3);
// Re-calculate density if structure assumed
// density_kg_per_m3 = (n_atoms * M_amu * amuToKg) / (V_cell_m3 * 1); // Mass per volume
} else if (eta >= 0.65) { // Approximate range for BCC
n_atoms = 2;
// For BCC, a = 4r/sqrt(3) => V_cell = (4r/sqrt(3))^3
V_cell_m3 = Math.pow(4 * r_m / Math.SQRT3, 3);
} else { // Assume SC or other low packing
n_atoms = 1;
V_cell_m3 = Math.pow(2 * r_m, 3); // SC approximation
}
// Recalculate based on assumed n and V_cell to check consistency
// The initial direct calculation `density_kg_per_m3 = (M_kg_per_mol * eta) / (NA * V_atom_m3);` is robust.
// Let's use derived V_cell based on assumed structure for display, and derived n.
// The density MUST be consistent. Let's use the primary calculation for display.
var display_V_cell = V_cell_m3; // Using the structure-derived volume
var display_n = n_atoms; // Using the structure-derived n
// Ensure the displayed density matches the primary result
// Recalculate density using these assumed V_cell and n for consistency IF needed.
// density_kg_per_m3 = (display_n * M_amu * amuToKg) / (display_V_cell * 1); // Mass in kg / Vol in m^3
// density_g_per_cm3 = density_kg_per_m3 * 0.001;
// Display results
primaryResult.textContent = density_g_per_cm3.toFixed(3) + " g/cm³";
volumeResult.textContent = display_V_cell.toExponential(3) + " m³"; // V_cell
molarMassInKg.textContent = (M_amu * amuToKg).toExponential(3) + " kg/mol"; // Molar mass in kg/mol
atomsPerUnitCell.textContent = display_n;
resultsContainer.style.display = 'block';
updateChart();
}
function resetCalculator() {
atomicRadiusInput.value = defaultAtomicRadius;
atomicWeightInput.value = defaultAtomicWeight;
packingEfficiencyInput.value = defaultPackingEfficiency;
atomicRadiusError.textContent = "";
atomicWeightError.textContent = "";
packingEfficiencyError.textContent = "";
resultsContainer.style.display = 'none';
if (densityChartInstance) {
densityChartInstance.destroy();
densityChartInstance = null;
}
}
function copyResults() {
var resultsText = "Density Calculation Results:\n\n";
resultsText += "Density: " + primaryResult.textContent + "\n";
resultsText += "Volume (Unit Cell): " + volumeResult.textContent + "\n";
resultsText += "Molar Mass: " + molarMassInKg.textContent + "\n";
resultsText += "Atoms per Unit Cell: " + atomsPerUnitCell.textContent + "\n\n";
resultsText += "Inputs Used:\n";
resultsText += "Atomic Radius: " + atomicRadiusInput.value + " pm\n";
resultsText += "Atomic Weight: " + atomicWeightInput.value + " amu\n";
resultsText += "Packing Efficiency: " + packingEfficiencyInput.value + "\n";
var textArea = document.createElement("textarea");
textArea.value = resultsText;
document.body.appendChild(textArea);
textArea.focus();
textArea.select();
try {
var successful = document.execCommand('copy');
var msg = successful ? 'Results copied!' : 'Copy failed!';
// console.log(msg); // Log to console or show a temporary message
var notification = document.createElement('div');
notification.textContent = msg;
notification.style.cssText = 'position: fixed; top: 70px; right: 20px; background-color: var(–primary-color); color: white; padding: 10px; border-radius: 5px; z-index: 1000;';
document.body.appendChild(notification);
setTimeout(function() {
notification.remove();
}, 2000);
} catch (err) {
// console.error('Fallback: Oops, unable to copy', err);
}
textArea.remove();
}
function toggleFaq(element) {
var paragraph = element.nextElementSibling;
if (paragraph.style.display === "block") {
paragraph.style.display = "none";
} else {
paragraph.style.display = "block";
}
}
// Charting Functionality
function updateChart() {
if (densityChartInstance) {
densityChartInstance.destroy();
}
var baseAtomicRadius = parseFloat(atomicRadiusInput.value) || defaultAtomicRadius;
var baseAtomicWeight = parseFloat(atomicWeightInput.value) || defaultAtomicWeight;
var basePackingEfficiency = parseFloat(packingEfficiencyInput.value) || defaultPackingEfficiency;
var radii = [];
var densities = [];
// Generate data points around the base input value
for (var i = -5; i <= 5; i++) {
var currentRadius = baseAtomicRadius + i * 10; // Vary radius by +/- 50 pm in steps of 10 pm
if (currentRadius <= 0) continue;
radii.push(currentRadius);
// Recalculate density for this radius, keeping other inputs constant
var r_m = currentRadius * 1e-12;
var V_atom_m3 = (4/3) * Math.PI * Math.pow(r_m, 3);
var M_kg_per_mol = baseAtomicWeight * 1.66053906660e-27 * 6.02214076e23;
var density_kg_per_m3 = (M_kg_per_mol * basePackingEfficiency) / (6.02214076e23 * V_atom_m3);
var density_g_per_cm3 = density_kg_per_m3 * 0.001;
densities.push(density_g_per_cm3);
}
densityChartInstance = new Chart(chartCanvas, {
type: 'line',
data: {
labels: radii.map(function(r) { return r.toFixed(0) + ' pm'; }), // Labels as pm
datasets: [{
label: 'Density (g/cm³)',
data: densities,
borderColor: 'rgb(0, 74, 153)', // Primary color
backgroundColor: 'rgba(0, 74, 153, 0.2)',
tension: 0.1,
fill: true
}]
},
options: {
responsive: true,
maintainAspectRatio: false,
scales: {
x: {
title: {
display: true,
text: 'Atomic Radius (pm)'
}
},
y: {
title: {
display: true,
text: 'Density (g/cm³)'
}
}
},
plugins: {
title: {
display: true,
text: 'Density vs. Atomic Radius (Fixed Atomic Weight & Packing Efficiency)'
}
}
}
});
}
// Initialize chart on load if inputs have default values
document.addEventListener('DOMContentLoaded', function() {
atomicRadiusInput.value = defaultAtomicRadius;
atomicWeightInput.value = defaultAtomicWeight;
packingEfficiencyInput.value = defaultPackingEfficiency;
// updateChart(); // Uncomment if you want the chart to load with default values initially
});
// Update results in real-time as inputs change
atomicRadiusInput.addEventListener('input', function() { if(resultsContainer.style.display === 'block') calculateDensity(); });
atomicWeightInput.addEventListener('input', function() { if(resultsContainer.style.display === 'block') calculateDensity(); });
packingEfficiencyInput.addEventListener('input', function() { if(resultsContainer.style.display === 'block') calculateDensity(); });