Electron Transition Energy Calculator

How to Use This Calculator

1. Enter the initial energy level (n₁) of the electron. This is the higher energy level the electron starts from.
2. Enter the final energy level (n₂) of the electron. This is the lower energy level the electron transitions to.
3. Enter the atomic number (Z) of the atom. For hydrogen, this is 1. For helium, this is 2, and so on.
4. Click the "Calculate" button to compute the energy of the transition and the corresponding wavelength.
5. The results will be displayed in electron volts (eV) and nanometers (nm).

Working Principle

This calculator uses the Rydberg formula to calculate the energy of an electron transition:

E = Z² × (13.6 eV) × (1/n₁² - 1/n₂²)

Where:

• E is the energy of the transition in electron volts (eV)
• Z is the atomic number of the atom
• n₁ is the initial energy level
• n₂ is the final energy level

The calculator also calculates the wavelength of the emitted or absorbed photon using the energy-wavelength relationship E = hc/λ, where h is Planck's constant and c is the speed of light.

Example

For a hydrogen atom (Z=1), if an electron transitions from n₁=3 to n₂=2:

1. Initial energy level (n₁) = 3
2. Final energy level (n₂) = 2
3. Atomic number (Z) = 1

Calculating the energy:

E = 1² × (13.6 eV) × (1/3² - 1/2²) = 10.2 eV

Calculating the wavelength:

λ = (4.135667696e-15 eV·s × 2.99792458e8 m/s) / 10.2 eV = 121.56 nm

This corresponds to a transition in the Lyman series of hydrogen with a wavelength in the ultraviolet region.