Quantum Model of the Atom

Scientists had discovered that light could behave both as a particle and as a wave French scientist Louis de Broglie suggested that electrons also had a dual wave-particle nature Electrons could be considered to be waves confined to a space around the nucleus The waves had to be certain frequencies, and thus had a certain amount of energy

A German physicist, Werner Heisenberg, explained that it is impossible to pinpoint a location for an electron in an atom Electrons are detected by their interaction with photons Photons have about the same amount of energy as electrons, so when a photon interacts with an electron, it knocks the electron off course

Heisenberg Uncertainty Principle It is impossible to determine simultaneously both the position and velocity of an electron or any other particle.

Austrian physicist Erwin Schrödinger developed a mathematical equation that treated electrons as waves. Only waves of specific energies, and therefore frequencies, provided solutions to the equation. These solutions were called wave functions. This confirmed Bohr’s theory of quantifiable energy levels for electrons in an atom

Schrödinger’s wave equation along with the Heisenberg Uncertainty Principle laid the foundation for modern quantum theory. Quantum theory is a mathematical description of wave properties of electrons and other very small particles.

They exist in 3-D regions called orbitals The wave functions resulting from Schrödinger’s Wave Equation give only the PROBABILITY of finding an electron at a given place around the nucleus. Therefore electrons don’t travel around the nucleus in orbits as in Bohr’s model They exist in 3-D regions called orbitals Orbitals come in different shapes and sizes The orbitals are actually electron clouds, or probable locations for electrons

Quantum numbers are used to describe the properties of atomic orbitals and the properties of electrons in those orbitals It takes 4 quantum numbers to describe the total energy state of each electron in an atom The first 3 quantum numbers indicate the main energy level, the shape, and the orientation of the orbital The 4th quantum number describes the spin state of the electron occupying the orbital

Principal Quantum Number Symbol is n Indicates the main energy level occupied by the electron Lowest energy level is 1 As n increases, the distance from the nucleus increases More than one electron can be in the same main energy level Sometimes main energy levels are called shells.

Angular Momentum Quantum Number Symbol is l Indicates the shape of the orbital At each main energy level there are n possible shapes At the first level there is 1 shape At the second level there are 2 shapes At the 3rd level there are 3 shapes At the 4th level there are 4 shapes

The shapes or orbitals are assigned letters s orbitals are spherical p orbitals are dumb-bell shaped d orbitals are more complex f orbitals are even more complex

Every atomic orbital is designated by both its principal quantum number and the letter representing its shape 1s orbital is the s-shaped orbital in the first main energy level 2s orbital is the s-shaped orbital in the second main energy level

Magnetic Quantum Number Symbol is m Indicates the orientation of the orbital around the nucleus s orbitals are spherical so they can only be oriented 1 way p orbitals can be oriented three ways Along the x-axis, the y-axis, and the z-axis

d orbitals can be oriented in 5 ways

f orbitals can be oriented in 7 ways

The total number of orbitals in a main energy level is n2 At the first energy level there is 1 orbital: 1s At the second energy level there are 4 orbitals: 2s, and three 2p orbitals At the third energy level there are 9 orbitals: 3s, three 3p orbitals, and five 3d orbitals At the fourth energy level there are 16 orbitals: 4s, three 4p orbitals, five 4d orbitals, and 7 4f orbitals.

Spin Quantum Number An electron in an orbital behaves like a planet spinning on its axis The electron exists in one of two spin states The spin quantum number indicates which of the two spin states the electron has. One orbital can only hold 2 electrons and they have opposite spin states.

Since each main energy level contains n2 orbitals, and each orbital can hold 2 electrons, then the number of electrons that can “fit” in each energy level is 2n2 The first energy level has 1 orbital and can hold 2 electrons The second energy level has 4 orbitals and can hold 8 electrons