The Quantum Mechanical Model of the Atom Chemistry 11 : The Quantum Mechanical Atom The Quantum Mechanical Model of the Atom Page

Rutherford’s Model of the Atom In 1911, Ernest Rutherford proposed the nuclear planetary model of the atom. In this model, most of the atom’s mass was located in a very small space in the centre of the atom (the nucleus – positively charged). Around the nucleus, electrons (negatively charged) orbited like planets orbiting the sun.

Problems with Rutherford’s Model In Classical physics, when a charged particle oscillates or accelerates, it gives off electromagnetic radiation (light energy). Since the electron is constantly accelerating (constantly changing its direction), it should give off light energy. But if an electron is giving off energy, it should slow and fall in towards the nucleus, causing the atom to collapse and to emit further radiation (calculated to be violet or ultraviolet light), ending in an “ultraviolet catastrophe”. Since atoms do not collapse in a burst of ultraviolet light, the planetary model had to be incorrect.

Bohr’s Model of the Atom Niels Bohr’s Model of the atom indicated that electrons were restricted to given energy levels or shells around an atom. Any given shell could hold at maximum, 2n2 electrons, where n = the energy level, a natural number from 1 to 2 to 3 etc. Thus the maximum number of electrons that could be contained on energy level 4 is 2(4)2 = 32. Bohr’s shells were given number and letter values: K (n=1), L (n=2), M (n=3), N (n=4) etc.

Bohr’s Model of the Atom Atoms absorb specific energies by sending electrons to specific higher energy levels and atoms emit specific energies (as light) when electrons drop to specific lower energy levels.

Problem With Bohr’s Model: It Only Explained The Hydrogen Atom Bohr’s Model failed to explain atoms besides Hydrogen. The bright line spectra of other atoms often break apart into smaller spectral lines in magnetic fields and Bohr’s atom could not explain this.

Einstein (1900) Suggested That Light Be Thought of as Energy Particles Louis De Broglie suggested that if energy could be thought of as particles, matter (electrons) could be thought of as waves. Electron “standing waves” would have specific wavelengths depending on their energy value and distance from the nucleus.

The Heisenburg Uncertainty Principle Heisenburg demonstrated that it was impossible to know both the position and speed of an electron since the energy used to detect this would alter both the position and speed of an electron, making it impossible to know these. This means that it is only possible to determine the probability of where an electron will be. The shape of the space where an electron is likely to be is called an orbital (as distinguished from an orbit which is a circular path, something that can not be because of the uncertainty principle).

The Heisenburg Uncertainty Principle

Erwin Schrodinger: Treated Electrons as Waves Treating electrons as waves and using complicated wave equations, Schrodinger was able to produce electron probability distributions for where an electron was likely to be located in space around the nucleus.

Where an electron is likely to be (Electron Probability Distribution) is determined by four quantum numbers which solve Schrodinger’s equations. The four quantum numbers are (n,l,m,s) These numbers are put into a wave equation and solve the equation, producing a three-dimensional representation (orbital) of where the electron is most likely to be. By analogy, we can locate a person on earth by (Country, Province, City, Street Address) which is like the quantum numbers (n,l,m,s)

n, the Principal Quantum Number The principal quantum number corresponds to Bohr’s energy shells. n is a natural number (1,2,3,4,5.etc.) n indicates how far from the nucleus the electron is likely to be. n refers to the major energy level an electron will be found in. Capital letters (K,L,M,N) also refer to the major energy levels.

l , the orbital (azimuthal) number The orbital number, l , (azimuthal number) refers to the minor energy level an electron is in, within its major energy level. The orbital number on a given major energy level is a whole number that goes from 0 to 1 to 2 to a maximum of n-1. For n=1, l = 0. For n=2, l = 0, 1. For n=3, l = 0, 1, 2. On a major energy level, there are as many minor energy levels as the value of n (ex: three minor energy levels on n=3, designated by l = 0, 1, 2.

Orbitals Orbitals are three-dimensional spaces in which electrons have a high probability of being found (99% chance). A single orbital can hold 0, 1, or 2 electrons.

l , the orbital (azimuthal) number Instead of numbers, l is usually denoted by letters. l=0 is referred to as s (spherical shaped orbital) l=1 is referred to as p (dumbbell-shaped orbitals) l=2 is referred to as d (many-shaped orbitals) l=3 is referred to as f (many-shaped orbitals)

Orbital Shapes l=0 is referred to as s (spherical shaped orbital) l=1 is referred to as p (dumbbell-shaped orbitals) l=2 is referred to as d (many-shaped orbitals) l=3 is referred to as f (many-shaped orbitals)

m, the magnetic quantum number m, the magnetic quantum number indicates the orientation of the orbital(s) in space as well as the number of orbitals on a minor energy level. m is an integer from –l to + l. The values for m depend on the l minor energy level. For l =0 (spherical shape), m=0 (One way to orient a sphere) For l =1 (dumbbell shapes), m= -1, 0, +1 (three ways to orient) For l =2 (many shapes), m= -2, -1, 0, 1, 2

Overview of Major Energy Levels, Minor Energy Levels and Orbitals The number of minor energy levels on a major energy level is n The number of orbitals on a major energy level (pel) is n2 The number of electrons accommodated on a pel is 2n2

s, the spin number s, the spin number, indicates whether an electron has a clockwise spin or a counterclockwise spin. s is a rational fraction of either +1/2 (clockwise) or -1/2 (counterclockwise).

Energy Levels and Orbitals The following diagram summarizes the energy levels and orbitals but does not properly show the relative energies of minor energy levels,

Energy Levels and Orbitals The following diagram summarizes energy levels and orbitals and shows the relative energies of minor energy levels,

Electrons in Atoms To show electron placement of an atom, determine the number of electrons from the atomic number (and ion charge for ions). Begin filling electrons from lowest to higher energy levels. Use Hund’s Rule for multiple orbitals on the same minor energy level: No orbital can have two electrons until each orbital has at least one electron.

Electrons in Atoms Use the Aufbau Principle to determine the order in which orbitals fill:

Orbital Diagrams and Electron Configurations Two common ways to show electron structure in atoms are orbital diagrams and electron configurations.

Ground State vs Excited Atoms A ground state atom has its electrons in the lowest possible orbitals and this atom has the lowest energy. An excited atom has one or more of its electrons in higher orbitals so that one or more lower electrons is unpaired or a lower orbital is empty.

The Orbitals of An Atom Are Overlayed in Space

d orbitals can borrow from lower s orbitals When d orbitals are one electron from being half-full or full, they borrow one electron from the next lowest s orbital to make a half-full or full d minor energy level. This is possible because d and s orbitals are very close in energy value. Ex: Cr and Cu

Chemical Families Explained by Quantum Mechanical Model Elements display similar chemical behaviour because they have the same electron configurations at different energy levels.

Magnetism Explained by Quantum Mechanical Model When atoms have a series of unpaired d orbitals, the magnetic effects of the unpaired electrons intensify and lead to the atom itself having a strong magnetic field. Neighboring magnetic atoms together intensify the overall magnetic fields of each other, creating microscopic regions of atoms called domains. Each domain has magnetic poles. Fe: 1s2 2s22p63s23p64s2 3d23d13d13d13d1

Quantum Mechanical Model and Periodic Chart The periodic chart is composed of blocks which reflect the quantum mechanical model of the atom

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