Calculate Photon Energy Between N

Calculate the energy of a photon emitted or absorbed when an electron transitions between two energy levels in an atom. This calculator uses the Rydberg formula to determine photon energy in electron volts (eV), joules (J), or other units.

Introduction

When an electron moves between energy levels in an atom, a photon is emitted or absorbed. The energy of this photon can be calculated using the Rydberg formula, which relates the energy to the principal quantum numbers of the initial and final states.

This calculation is fundamental in atomic physics and spectroscopy. Understanding photon energy helps in analyzing atomic spectra, designing lasers, and studying quantum transitions.

Photon Energy Formula

The energy of a photon emitted or absorbed during a transition between energy levels n1 and n2 is given by:

E = hc / λ = R∞hc (1/n1² - 1/n2²)

Where:

E = Photon energy
h = Planck's constant (6.62607015 × 10⁻³⁴ J·s)
c = Speed of light in vacuum (2.99792458 × 10⁸ m/s)
λ = Wavelength of the photon
R∞ = Rydberg constant (1.0973731568160 × 10⁷ m⁻¹)
n1 = Principal quantum number of the initial state
n2 = Principal quantum number of the final state

For hydrogen-like atoms, the formula simplifies to:

E = 13.6 eV (1/n1² - 1/n2²)

This simplified form assumes n1 > n2 for photon emission (n1 = 3, n2 = 2) or n1 < n2 for photon absorption (n1 = 2, n2 = 3).

How to Use This Calculator

Enter the initial principal quantum number (n1) for the electron's starting state.
Enter the final principal quantum number (n2) for the electron's ending state.
Select the desired output unit (eV, J, or others).
Click "Calculate" to compute the photon energy.
Review the result and interpretation.

Note: For photon emission, n1 must be greater than n2. For photon absorption, n1 must be less than n2.

Worked Example

Calculate the photon energy when an electron transitions from n1 = 3 to n2 = 2 in a hydrogen atom.

Using the simplified formula:

E = 13.6 eV (1/3² - 1/2²) = 13.6 eV (1/9 - 1/4) = 13.6 eV (0.1111 - 0.25) = 13.6 eV (-0.1389) = -1.887 eV

The negative sign indicates energy is released (photon emission). The absolute value is 1.887 eV.

In joules: 1.887 eV × 1.60218 × 10⁻¹⁹ J/eV ≈ 3.03 × 10⁻¹⁹ J.

Frequently Asked Questions

What is the difference between photon emission and absorption?

Photon emission occurs when an electron moves to a lower energy level (n1 > n2), releasing energy as a photon. Photon absorption occurs when an electron moves to a higher energy level (n1 < n2), absorbing energy from a photon.

Why is the Rydberg formula used for hydrogen-like atoms?

The Rydberg formula is derived from the Bohr model of the hydrogen atom and can be generalized to hydrogen-like atoms (single-electron ions) where the nuclear charge equals the atomic number.

What units should I use for photon energy?

Electron volts (eV) are commonly used in atomic physics, while joules (J) are the SI unit. The calculator provides both options for your convenience.