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**Section 2: Quantum Theory and the Atom**

Electrons in atoms Section 2: Quantum Theory and the Atom

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Learning Goals Compare the Bohr and quantum mechanical models of the atom. Explain the impact of de Broglie’s wave particle duality and the Heisenberg uncertainty principle on the current view of electrons in atoms. Identify the relationships among a hydrogen atom’s energy levels, sublevels, and atomic orbitals.

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**Bohr’s Model of the Atom**

Einstein’s theory of light’s dual nature accounted for several unexplainable phenomena, but it did not explain why atomic emission spectra of elements were discontinuous.

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**Bohr’s Model of the Atom**

In 1913, Niels Bohr, a Danish physicist working in Rutherford’s laboratory, proposed a quantum model for the hydrogen atom that seemed to answer this question. This model correctly predicted the frequency lines in hydrogen’s atomic emission spectrum.

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**Bohr’s Model of the Atom**

The lowest allowable energy state of an atom is called its ground state. When an atom gains energy, it is in an excited state.

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**Bohr’s Model of the Atom**

Bohr suggested that an electron moves around the nucleus only in certain allowed circular orbits.

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**Bohr’s Model of the Atom**

Each orbit was given a number, called the quantum number.

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**Bohr’s Model of the Atom**

Hydrogen’s single electron is in the n = 1 orbit in the ground state. When energy is added, the electron moves to the n = 2 orbit.

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**Bohr’s Model of the Atom**

The electron releases energy as it falls back towards the ground state.

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**Bohr’s Model of the Atom**

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**Bohr’s Model of the Atom**

Bohr’s model explained the hydrogen’s spectral lines, but failed to explain any other element’s lines. The behavior of electrons is still not fully understood, but it is known they do not move around the nucleus in circular orbits.

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**Quantum Mechanical Model**

Louis de Broglie (1892–1987) hypothesized that particles, including electrons, could also have wavelike behaviors. Electrons orbit the nucleus only in whole-number wavelengths.

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**Quantum Mechanical Model**

If electrons can only orbit in whole number wavelengths, then only certain frequencies and energies are possible. Not possible to have a continuous spectrum.

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**Quantum Mechanical Model**

The de Broglie equation predicts that all moving particles have wave characteristics.

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**Quantum Mechanical Model**

Heisenberg showed it is impossible to take any measurement of an object without disturbing it. The Heisenberg uncertainty principle states that it is fundamentally impossible to know precisely both the velocity and position of a particle at the same time.

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**Quantum Mechanical Model**

The only quantity that can be known is the probability for an electron to occupy a certain region around the nucleus.

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**Quantum Mechanical Model**

Schrödinger treated electrons as waves in a model called the quantum mechanical model of the atom. Schrödinger’s equation applied equally well to elements other than hydrogen (unlike Bohr’s model).

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**Quantum Mechanical Model**

The quantum mechanical model makes no attempt to predict the path of an electron around the nucleus.

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**Quantum Mechanical Model**

Instead, Schrödinger’s wave function predicts a three-dimensional region around the nucleus called the atomic orbital in which an electron may be found.

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**Hydrogen’s Atomic Orbitals**

Principal quantum number (n) indicates the relative size and energy of atomic orbitals. n specifies the atom’s major energy levels, called the principal energy levels.

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**Hydrogen’s Atomic Orbitals**

Energy sublevels are contained within the principal energy levels.

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**Hydrogen’s Atomic Orbitals**

Each energy sublevel relates to orbitals of different shape. s, p, d, f s, p, d s, p s

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**Hydrogen’s Atomic Orbitals**

s sublevel:

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**Hydrogen’s Atomic Orbitals**

p sublevel:

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**Hydrogen’s Atomic Orbitals**

d sublevel:

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**Hydrogen’s Atomic Orbitals**

f sublevel:

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**Hydrogen’s Atomic Orbitals**

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**Hydrogen’s Atomic Orbitals**

At any given time, hydrogen’s electron can occupy just one orbital. When hydrogen is in the ground state, the electron occupies the 1s orbital. When the atom gains a quantum of energy, the electron is excited to one of the unoccupied orbitals.

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