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Particle In A Box Calculator

Calculate de Broglie matter wavelength λ = h/p, photon energy E = hf, Bohr hydrogen energy levels, Heisenberg uncertainty ΔxΔp ≥ ħ/2, and photoelectric work function for particle in a box.

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Input Quantum Parameters

Enter principal quantum number n, wavelength λ, or frequency f.

Calculated Photon Energy (E)

2.48 eV
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Planck-Einstein Relation

Photon energy is quantized: E = h × f = (h × c) / λ. In electronvolts: E(eV) ≈ 1240 / λ(nm). Green light at 500 nm delivers 2.48 eV per photon.

Calculation Methodology & Details

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Formula

de Broglie Wavelength: λ = h / p = h / (m × v) Bohr Energy Levels: E_n = -13.6 eV / n² Photoelectric Effect: K_max = h × f - Φ Heisenberg Uncertainty: Δx × Δp ≥ ħ / 2 Schrödinger Time-Independent: Ĥ Ψ = E Ψ

Applies Planck's constant h = 6.626 × 10⁻³⁴ J·s, Bohr hydrogen atom quantization, Compton scattering shifts, and Pauli exclusion spin matrices.

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Important Disclaimer

Calculations assume non-relativistic quantum states unless Dirac equation or relativistic de Broglie momentum γmv is specified.

How to Calculate Step-by-Step

Follow these steps to complete the calculation:

1

Step 1

Enter photon wavelength λ (nm) or frequency f (THz).

2

Step 2

Specify principal quantum number n (1, 2, 3...) or work function Φ (eV).

3

Step 3

View photon energy in electronvolts (eV) and Joules, de Broglie matter wavelength, or hydrogen orbital energy level.

Detailed Insights & Expert Guide

ℹ️ About this Calculation

The Particle In A Box Calculator solves de Broglie matter-wave dualism, photoelectric kinetic energy emission, Bohr atom hydrogen spectral energy levels, Heisenberg position-momentum uncertainty, and Schrödinger wave equation tunneling probability.

Variable Glossary

Input

Planck's Constant (h)

Fundamental quantum constant h ≈ 6.62607015 × 10⁻³⁴ J·s (ħ = h / 2π = 1.0545718 × 10⁻³⁴ J·s).

Parameter

Electronvolt (eV)

Unit of energy equal to kinetic energy gained by an electron accelerating through 1 Volt: 1 eV = 1.602176634 × 10⁻¹⁹ Joules.

FAQ

What is the Photoelectric Effect?
Discovered by Hertz and explained by Einstein in 1905, light photons strike a metal surface to eject electrons if photon energy E = hf exceeds the metal's binding work function Φ: K_max = hf - Φ.
What is the de Broglie Wavelength?
Louis de Broglie hypothesized that all matter has wave-like properties with wavelength λ = h / p. Electrons accelerated through 100 Volts have a de Broglie wavelength of ~0.12 nm, comparable to X-rays and crystal lattice spacing.
What is Quantum Tunneling?
Quantum tunneling is the wave-mechanical phenomenon where a particle's wave function has a non-zero transmission probability T ≈ exp(-2K L) to penetrate through a potential energy barrier higher than the particle's kinetic energy.