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**The Quantum Model of the Atom**

Section 4-2 Pages

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**Hydrogen-Atom Line-Emission Spectrum**

Ground state – the lowest energy state of an atom Excited state – a state in which an atom has a higher potential energy than it has in its ground state

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Continued Continuous spectrum – the emission of a continuous range of frequencies of electromagnetic radiation Line-emission spectrum – when a narrow beam of the emitted light was shined through a prism, it is separated into a series of specific frequencies of visible light

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**Niels Bohr Danish physicist**

Proposed a model of the hydrogen atom that linked the atom’s electron with photon emission Electron can circle the nucleus only in allowed paths, orbits Electron can neither gain nor lose energy “the single electron of hydrogen orbits the nucleus only in allowed orbits, each with a fixed energy”

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Electrons as Waves -de Broglie found that electrons have wave-like properties: -diffraction – bending of a wave as it passes by the edge of an object -interference – a reduction or increase in energy when waves overlap Heisenberg Uncertainty Principle: it is impossible to determine simultaneously both the position and velocity of an electron or any other particle

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Quantum Theory -describes mathematically the wave properties of electrons and other very small particles

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**Atomic Orbitals and Quantum Numbers**

Orbital – three-dimensional region around the nucleus that indicates the probable location of an electron (each orbital can contain 2 electrons) Quantum numbers – specify the properties of atomic orbitals and the properties of electrons in orbitals

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Quantum Numbers Each electron in an atom can be characterized by four quantum numbers. No two electrons have the same 4 quantum numbers. These numbers are known as the Principal, Angular Momentum, Magnetic, and Spin Quantum Numbers.

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**Principal Quantum Number**

Symbolized by n, indicates the main energy level occupied by the electron Positive values of 1,2,3,… As n increases, e- energy and distance from the nucleus increase n=1, first, or lowest, main energy level is closest to the nucleus Electrons with the same n value are said to be in the same shell Total number of orbitals per shell or main energy level is n squared Most general of all quantum #s; like saying, “Where do you live,” and I answer, “in Texas.”

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**Angular Momentum Quantum Number**

-symbolized by l, indicates the shape of the orbital -known as a sublevel -the # of orbital shapes possible is equal to n -values are zero and positive integers less than or equal to n-1 (0 = s, 1 = p, 2 = d, 3 = f) -s orbitals are spherical; p orbitals are dumbbell shaped; d and f orbitals are more complex -value of n = # of sublevels. Ex: nth main energy level is n sublevels -each orbital is designated by its principal quantum # followed by the letter of the sublevel. Ex: 2p = set of p orbitals in the 2nd main energy level -more specific such as “I live in Canyon, TX.”

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**Magnetic Quantum Number**

-symbolized by m, indicates the orientation of an orbital around the nucleus -s orbital, m = 0; only one possible orientation (only one orbital/s sublevel) -p orbitals extend along x, y, and z axis (3-D) therefore there are 3 orbitals/p sublevel) -designated px, py, and pz -m = -1, m = 0, m = +1 -d orbitals, 5/d sublevel -m = -2, -1, 0, +1, +2 -f orbitals, 7/f sublevel # of orbitals = n squared. Ex: 3rd energy level = 3 squared = 9 orbitals -even more specific; like saying “I live at #3 Summit Drive, Canyon, TX”

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**Spin Quantum Number -orbitals spin on an internal axis**

-two possible directions (clockwise, counterclockwise) -spin creates a magnetic field -only 2 possible values (+1/2, -1/2) which indicate 2 fundamental spin states of an electron in an orbital -each orbital can hold 2 electrons, which must have opposite spins -maximum # of electrons per energy level = 2n squared

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**Check it Out Is this set of quantum numbers possible? 3,3,-2, -1/2**

No, l must be 2 or less. What could l be if n is equal to 5? 4, 3, 2, 1, 0

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