Bohr’s model of the hydrogen atom

Bohr s model of the hydrogen atom. Identification of atomic number with nuclear charge number (H. Moseley). 

In Bohr s model of the hydrogen atom, the circular orbits were determined by the quantum number more accurately, by the square of the quantum number n. No other orbits were allowed. By changing the orbits from circles to ellipses, Sommerfeld introduced a second radius, which gave him another variable to play with. So it was that Sommerfeld generalized Bohr s quantum condition for electron orbits in terms of the two quantum numbers n and k. His analysis led him to establish a relationship between the two quantum numbers namely, the quantum number n set the upper limit on the quantum number k, but k could have smaller values as follows ... 

Sommerfeld s work was based on Bohr s model of the hydrogen atom. In this work, he brought relativity theory and the quantum idea together and was able to account for the fine details of the hydrogen spectrum. After Sommerfeld s paper on this work was published in 1916, he received a letter from Niels Bohr. In it Bohr wrote, I do not believe ever to have read anything with more joy than your beautiful work. ... 

Like Bohr s model of the hydrogen atom, Sommerfeld s theory flowered only briefly. The creation of quantum mechanics and the discovery of electron spin, both in 1925, followed by Paul Dirac s theory in 1928, provided a solid theory-based underpinning for... 

The first sentence of Schrodinger s classic paper reads as follows In this paper I wish to consider, first, the simplest case of the hydrogen atom, and show that the customary quantum conditions can be replaced by another posmlate, in which the notion of whole numbers, merely as such, is not introduced. Two things about this sentence are noteworthy. First, an explanation of the hydrogen atom is clearly the objective of Schrodinger s wave mechanics. Second, in the development that follows this introductory sentence, quantum numbers ( whole numbers ), which appeared in Bohr s model of the hydrogen atom in a somewhat ad hoc fashion, appear as a namral consequence of Schrodinger s physical and mathematical approach. 

I See the Saunders Interactive General Chemistry CD-ROM, Screen 7.7, Bohr s Model of the Hydrogen Atom. 

OBJECTIVE To learn about Bohr s model of the hydrogen atom. 

These two situations are summarized in T Figure 6.13. We see that Bohr s model of the hydrogen atom leads to the conclusion that only the specific frequencies of light that satisfy Equation 6.7 can be absorbed or emitted by the atom. 

Bohr s model of the hydrogen atom explained observed spectral lines so well that many scientists concluded that the model could be applied to all atoms. It was soon recognized, however, that Bohr s approach did not explain the spectra of atoms with more than one electron. Nor did Bohr s theory explain the chemical behavior of atoms. 

To the scientists of the eariy twentieth century. Bohr s model of the hydrogen atom contradicted common sense. Why did hydrogen s electron exist around the nucleus only in certain allowed orbits with definite energies Why couldn t the electron exist in a limitless number of orbits with slightly different energies ... 

In Bohr s model of the hydrogen atom, only one number, n, was necessary to describe the location of the electron. In quantum mechanics, three quantum numbers are required to describe the distribution of electron density- in an atom. These numbers are derived from the mathematical solution of Schrbdinger s equation for the hydrogen atom. They are called the principal quantum number, the angular momentum quantum number, and the magnetic quantum number. Each atomic orbital in an atom is characterized by a unique set of these three quantum numbers. 

Modern quantum theory, also called quantum physics or quantum mechanics, replaced Bohr s theory in 1926. Quantization arises naturally by using quantum mechanics. It is not assumed or imposed beforehand as a condition, as was done by Bohr. As we will soon see, the circular orbits that are so prominent in Bohr s model of the hydrogen atom are absent in the model based on quantum mechanics. Despite the fact that Bohr s model of the hydrogen atom is wrong, it was an important scientific development because it prompted a paradigm shift—the quantum leap—from classical physics to the new quantum physics. 

The uncertainty relation AxAp s h/ iTr), expression (8.11), is valid for motion in any direction. For circular motion, the relation may be expressed as ArAp > /z/(4tt), where Ar is the uncertainty in radial position and Ap is the uncertainty in the momentum along the radial direction. Describe how Bohr s model of the hydrogen atom violates the uncertainty relation expressed in the form ArAp > hl 7r). 

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