Bohr Model Calculator

The Bohr model describes an atom as a small, positively charged nucleus surrounded by electrons traveling in circular orbits. When an electron jumps between these fixed energy levels, it absorbs or emits a photon. This calculator relies on two primary physical relationships. First, the energy difference between two orbits is calculated using the equation ΔE = E_higher - E_lower, where E_higher represents the outer orbit and E_lower represents the inner orbit. Second, the frequency (f) of the resulting photon is determined using Planck's relation, f = ΔE / h, where h is Planck's constant (approximately 6.62607 × 10^-34 joule-seconds).

Imagine an electron in a hydrogen atom dropping from a higher energy level of -3.40 eV to a lower energy level of -13.60 eV. To find the energy difference, convert electron-volts to joules (1 eV = 1.602 × 10^-19 J). The higher energy is -5.448 × 10^-19 J and the lower energy is -2.179 × 10^-18 J. Subtracting the lower energy from the higher energy yields an energy difference (ΔE) of 1.634 × 10^-18 Joules. Next, divide this energy difference by Planck's constant (6.62607 × 10^-34 J·s). This gives a photon frequency of approximately 2.466 × 10^15 Hz, characterizing the ultraviolet light emitted during this specific quantum transition.

Always verify your units before plugging numbers into atomic formulas. Energy values in quantum physics are frequently expressed in electron-volts (eV) but must be converted to Joules when computing absolute frequencies using Planck's constant. Additionally, remember that energy levels in bound atomic systems are negative because they represent a deficit compared to a free electron at infinite separation.