An excited hydrogen atom returns to its ground state. What is the possible energy change for the atom ?

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pacorz | High School Teacher | (Level 3) Educator

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Electrons are found in spcific energy levels, which reflect their motion and location in relation to the nucleus. Hydrogen has just one electron, so it is the easiest element to study to learn about this. Normally the electron of a hydrogen atom is located in the s sublevel of the first energy level. This is called the ground state.

When an electron absorbs a quantum (packet) of energy, it temporarily leaves the ground state orbital. In order to return to the ground state, it must re-emit that energy. Picture holding a ball in your hand, tossing it up in the air, and catching it again. The ball will rest in your hand until you impart kinetic energy to it. At that point it will leave your hand, but will eventually drop back down, transferring the energy, in the form of momentum, back into your hand.

The different energy levels of a Hydrogen atom are given by the equation:

E = - E0 n2

where E0 = 13.6 electronVolts (1 eV = 1.602×10-19 Joules) and n = 1,2,3… and so on, so that the ground state has energy E1= -13.6 eV, and the second energy level, which is also the first excited state, has energy E2 = -13.6/4 eV = -3.4 eV. We ignore the sign and use the absolute values of the numbers, so your elctron returning to ground state must emit the difference between the energies of the first and second levels: 13.6eV - 3.4eV = 10.2eV.

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