Hydrogen energy quantization

B Bohr s orbits that explained hydrogen s quantized energy states... 

In addition to the indirect relations between orbitals and spectroscopy, by means of the wavefunction of the system, there are direct connections that can be estabhshed. The very concept of energy quantization applied to particles of matter, intimately related to the orbital concept, is deeply rooted in spectroscopy in particular the emission spectrum of atomic hydrogen. 

So we can conclude that all hydrogen atoms have the same set of discrete energy levels. We say the energy levels of hydrogen are quantized. That is, only certain values are allowed. Scientists have found that the energy levels of all atoms are quantized. 

What experimental evidence do scientists have that the energy levels of hydrogen are quantized ... 

Quasiclassical calculations are similar to classical trajectory calculations with the addition of terms to account for quantum effects. The inclusion of tunneling and quantized energy levels improves the accuracy of results for light atoms, such as hydrogen transfer, and lower-temperature reactions. 

We see that, as L (the length of the box) or m (the mass of the particle) increases, the separation between neighboring energy levels decreases (Fig. 1.26). That is why no one noticed that energy is quantized until they investigated very small systems such as an electron in a hydrogen atom the separation between levels is so small for ordinary particles in ordinary-sized vessels that it is completely undetectable. We can, in fact, ignore the quantization of the motion of the atoms of a gas in a typical flask. 

The most important quantized property of an atomic electron is its energy. The quantum number that indexes energy is the principal quantum number (n). Eor the simplest atom, hydrogen, we can use Equation to calculate... 

The discovery of two other series of emission lines of hydrogen came later. They are named for their discoverers the Lyman series in the ultraviolet range and Paschen series in the infrared region. Although formulas were devised to calculate the spectral lines, the physics behind the math was not understood until Niels Bohr proposed his quantized atom. Suddenly, the emission spectrum of hydrogen made sense. Each line represented the energy released when an excited electron went from a higher quantum state to a lower one. 

Solving equation (6.21) for the energy E and replacing A by n, we obtain the quantized energy levels for the hydrogen-like atom... 

As the integers if and / both begin at zero, y = 1,2,3... can of course be identified as the principal quantum number n for the hydrogen atom (see Section 6.6.1). Thus, the quantization of the energy is due to the termination of the series, a condition imposed to obtain an acceptable solution. The associated Laguerre polynomials provide quantitative descriptions of the radial part of the wave functions for the hydrogen atom, as described in Appendix IV. 

The first application of quantum theory to a problem in chemistry was to account for the emission spectrum of hydrogen and at the same time explain the stability of the nuclear atom, which seemed to require accelerated electrons in orbital motion. This planetary model is rendered unstable by continuous radiation of energy. The Bohr postulate that electronic angular momentum should be quantized in order to stabilize unique orbits solved both problems in principle. The Bohr condition requires that... 

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