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Transition: n = 3 โ†’ n = 2
n = 1n = 2n = 3n = 4n = 5+

Live Telemetry & Summary

Observe the electron jump. Moving to a lower orbit emits a photon with energy equal to the orbit difference. Moving to a higher orbit requires absorbing a photon of the exact same energy.

Initial Energy (E_in):-1.511 eV
Final Energy (E_fin):-3.400 eV
Energy Difference (ฮ”E):-1.889 eV
Photon Color / ฮป:656.5 nm

Variable Adjuster

Initial Shell (n_in)3
15
Final Shell (n_fin)2
15

Bohr Hydrogen Atom

BOHR

The Bohr Model of the atom introduces quantized energy levels for electrons. Electrons orbit the nucleus in stable circular shells without radiating energy. They transition between shells by absorbing or emitting a photon of energy exactly equal to the difference between orbit energy levels.

En=โˆ’13.6n2 eV,ฮ”E=hf=hcฮปE_n = -\frac{13.6}{n^2}\text{ eV}, \quad \Delta E = hf = \frac{hc}{\lambda}

Whiteboard Solver Steps

Step 1

Energy Levels

The electron energy levels are quantized, depending inversely on the square of the quantum number n.

En=โˆ’13.6n2 eVE_n = -\frac{13.6}{n^2}\text{ eV}
Step 2

Initial and Final Orbit Energies

Energies of the electron in its starting and ending states.

Ein=โˆ’13.632=โˆ’1.511 eV,Efin=โˆ’13.622=โˆ’3.400 eVE_{in} = -\frac{13.6}{3^2} = -1.511\text{ eV}, \quad E_{fin} = -\frac{13.6}{2^2} = -3.400\text{ eV}
Step 3

Transition Energy (ฮ”E) & Photon Wavelength (ฮป)

Because the final energy is lower, a photon is emitted with energy equal to 1.889 eV.

ฮ”E=Efinโˆ’Ein=โˆ’1.889 eV,ฮป=1240โˆฃฮ”Eโˆฃ=656.5 nm\Delta E = E_{fin} - E_{in} = -1.889\text{ eV}, \quad \lambda = \frac{1240}{|\Delta E|} = 656.5\text{ nm}