De Broglie Wavelength Calculator

De Broglie Wavelength Calculator .db-calculator-container { font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Helvetica, Arial, sans-serif; max-width: 800px; margin: 0 auto; padding: 20px; background-color: #f9f9f9; border: 1px solid #e0e0e0; border-radius: 8px; box-shadow: 0 4px 6px rgba(0,0,0,0.05); } .db-calculator-container h2 { text-align: center; color: #2c3e50; margin-bottom: 25px; } .db-input-group { margin-bottom: 20px; background: #ffffff; padding: 15px; border-radius: 6px; border: 1px solid #eee; } .db-input-group label { display: block; margin-bottom: 8px; font-weight: 600; color: #34495e; } .db-input-group select, .db-input-group input { width: 100%; padding: 10px; border: 1px solid #ccc; border-radius: 4px; font-size: 16px; box-sizing: border-box; /* Fix padding issues */ } .db-input-group .db-hint { font-size: 12px; color: #7f8c8d; margin-top: 5px; } .db-btn { display: block; width: 100%; padding: 12px; background-color: #3498db; color: white; border: none; border-radius: 4px; font-size: 18px; font-weight: bold; cursor: pointer; transition: background-color 0.3s; } .db-btn:hover { background-color: #2980b9; } .db-result-box { margin-top: 25px; padding: 20px; background-color: #e8f6f3; border: 1px solid #a3e4d7; border-radius: 6px; display: none; } .db-result-item { display: flex; justify-content: space-between; margin-bottom: 10px; border-bottom: 1px solid #d1f2eb; padding-bottom: 5px; } .db-result-item:last-child { border-bottom: none; } .db-result-label { font-weight: 600; color: #16a085; } .db-result-value { font-family: "Courier New", Courier, monospace; font-weight: bold; color: #2c3e50; } .db-content-section { margin-top: 40px; line-height: 1.6; color: #333; } .db-content-section h3 { color: #2c3e50; border-bottom: 2px solid #3498db; padding-bottom: 10px; margin-top: 30px; } .db-content-section p { margin-bottom: 15px; } .db-content-section code { background-color: #f0f0f0; padding: 2px 5px; border-radius: 3px; font-family: monospace; } /* Grid for mass inputs to handle scientific notation visually if needed, strictly simpler here */

De Broglie Wavelength Calculator

Custom Mass Electron Proton Neutron Alpha Particle Baseball (0.145 kg)
You can use scientific notation (e.g., 1.5e-27)
Must be greater than 0 and less than speed of light (3e8)

Results

Wavelength ($\lambda$) [Meters]:
Wavelength [Nanometers]:
Wavelength [Angstroms]:
Momentum ($p$):

What is the De Broglie Wavelength?

The De Broglie Wavelength is a fundamental concept in quantum mechanics that describes the wave-like nature of matter. Proposed by Louis de Broglie in 1924, this hypothesis suggests that particles of matter (such as electrons) have dual properties: they act as particles and as waves.

This calculator helps you determine the wavelength associated with a massive particle moving at a specific velocity. This concept is crucial for understanding electron microscopy and quantum physics.

The De Broglie Equation

The wavelength ($\lambda$) is calculated using the following formula:

$\lambda = \frac{h}{p} = \frac{h}{m \cdot v}$

Where:

  • $\lambda$ (lambda): The wavelength of the particle (in meters).
  • $h$: Planck's Constant ($\approx 6.626 \times 10^{-34} \text{ J}\cdot\text{s}$).
  • $p$: The momentum of the particle.
  • $m$: The mass of the particle (in kilograms).
  • $v$: The velocity of the particle (in meters per second).

How to Use This Calculator

1. Select a Particle: Choose a common particle like an Electron or Proton from the dropdown menu to auto-fill the mass, or select "Custom Mass" to enter your own value.
2. Enter Velocity: Input the speed at which the particle is traveling in meters per second (m/s).
3. Calculate: Click the button to see the resulting wavelength in meters, nanometers (nm), and Angstroms ($\mathring{A}$).

Example Calculation

Imagine an electron (mass $\approx 9.11 \times 10^{-31}$ kg) moving at $1 \times 10^6$ m/s.

Using the formula: $\lambda = (6.626 \times 10^{-34}) / (9.11 \times 10^{-31} \times 10^6)$.
The result would be approximately $7.27 \times 10^{-10}$ meters, or roughly 7.27 Angstroms.

// Constants var PLANCK_CONSTANT = 6.62607015e-34; // J*s // Function to update mass based on dropdown selection function updateMassInput() { var particleSelect = document.getElementById("db_particle"); var massInput = document.getElementById("db_mass"); if (particleSelect.value !== "custom") { massInput.value = particleSelect.value; // Highlight the change visually slightly massInput.style.backgroundColor = "#e8f6f3"; setTimeout(function() { massInput.style.backgroundColor = "#fff"; }, 300); } else { massInput.value = ""; massInput.focus(); } } // Main Calculation Function function calculateDeBroglie() { // Clear previous error var errorDiv = document.getElementById("db_error"); var resultDiv = document.getElementById("db_result"); errorDiv.style.display = "none"; resultDiv.style.display = "none"; // Get Input Values var massVal = document.getElementById("db_mass").value; var velocityVal = document.getElementById("db_velocity").value; // Validation Logic if (massVal === "" || velocityVal === "") { errorDiv.innerHTML = "Please enter both Mass and Velocity."; errorDiv.style.display = "block"; return; } var mass = parseFloat(massVal); var velocity = parseFloat(velocityVal); if (isNaN(mass) || isNaN(velocity)) { errorDiv.innerHTML = "Please enter valid numeric values."; errorDiv.style.display = "block"; return; } if (mass <= 0) { errorDiv.innerHTML = "Mass must be greater than zero."; errorDiv.style.display = "block"; return; } if (velocity = speedOfLight) { errorDiv.innerHTML = "Warning: Velocity exceeds the speed of light. This calculator uses non-relativistic formulas, results may be physically impossible."; errorDiv.style.display = "block"; // We continue calculation but show warning } // Calculation: lambda = h / (m * v) var momentum = mass * velocity; var wavelengthMeters = PLANCK_CONSTANT / momentum; // Conversions var wavelengthNano = wavelengthMeters * 1e9; var wavelengthAngstrom = wavelengthMeters * 1e10; // Formatting Results (Scientific notation for very small/large numbers) // Helper to format nicely function formatSci(num) { if (num === 0) return "0"; if (num 10000) { return num.toExponential(4); } return num.toPrecision(5); } document.getElementById("res_meters").innerHTML = formatSci(wavelengthMeters) + " m"; document.getElementById("res_nanometers").innerHTML = formatSci(wavelengthNano) + " nm"; document.getElementById("res_angstroms").innerHTML = formatSci(wavelengthAngstrom) + " Å"; document.getElementById("res_momentum").innerHTML = formatSci(momentum) + " kg&cdot;m/s"; // Show Result resultDiv.style.display = "block"; }

Leave a Reply

Your email address will not be published. Required fields are marked *