Bohr model

In atomic physics, the Bohr model depicts the atom as a small, positively charged nucleus surrounded by electrons in orbit - similar in structure to the solar system. Because of its simplicity, the Bohr model is still commonly taught to introduce students to quantum mechanics.

Transitions between energy levels (Rydberg Formula)

When the electron moves from one energy level to another, a photon is given off. Using the derived formula for the different 'energy' levels of Hydrogen we can now determine the 'wavelengths' of light that a Hydrogen atom can give off.

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First, the energy of photons that a Hydrogen atom can give off are given by the difference of two Hydrogen energy levels:

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::E=E_i-E_f=rac{m_e e^4}{8 h^2 epsilon_{0}^2} left( rac{1}{n_{f}^2} - rac{1}{n_{i}^2} ight) ,

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:where n_f means the final energy level, and n_i means the initial energy level. (We are assuming the final energy level is less than the initial energy level.)

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And since the energy of a photon is

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::E=rac{hc}{lambda} ,

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The wavelength of the photon given off is

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::rac{1}{lambda}=rac{m_e e^4}{8 c h^3 epsilon_{0}^2} left( rac{1}{n_{f}^2} - rac{1}{n_{i}^2} ight) ,

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:also known as the Rydberg formula.

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This formula was known by scientists who did spectroscopy in the nineteenth century, but they had no theoretical justification for the formula until Bohr derived it this way.

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