Section 1: Revising the Atomic Model Energy Levels in Atoms Limitations of Rutherford’s Atomic Model Rutherford used existing ideas about the atom and proposed an atomic model in which the electrons move around the nucleus like the planets move around the sun. Rutherford’s model of the Atom only explained only a few simple properties of the atom. Explaining what leads to chemical properties of elements required a model that better described the behavior of electrons in atoms.

Section 1: Revising the Atomic Model The Bohr Model In 1913, Niels Bohr developed a new atomic model. Changed Rutherford’s model to incorporate newer discoveries about how the energy of an atom changes when the atom absorbs or emits light. Bohr proposed that an electron is found only in specific circular paths, or orbits, around the nucleus.

Section 1: Revising the Atomic Model Each possible electron orbit in Bohr’s model has a fixed energy. The fixed energies of an electron can have are called energy levels and are like rungs of a ladder. The lowest rung corresponds to the lowest energy level. An electron can move from one energy level to another but cannot exist between energy levels. To move from one energy level to another, an electron must gain or lose just the right amount of energy.

Niels Bohr (1913): e– can possess only certain amounts of energy, and can therefore be only certain distances from nucleus. e– found here e– never found here planetary (Bohr) model N

Section 1: Revising the Atomic Model A quantum of energy is the amount of energy required to move an electron from one energy level to another energy level. The energy of an electron is therefore said to be quantized. The quantum of energy required to move from one energy level to another is reduced the further the electron is from the nucleus. While the Bohr model provided results in agreement with experiments using the hydrogen atom, it failed to explain the energies absorbed and emitted by atoms with more than one electron.

Section 1: Revising the Atomic Model The Quantum Mechanical Model The Rutherford model and the Bohr model of the atom described the paths of a moving electron as you would describe the path of a large moving object. In 1926, Erwin Schrodinger used these calculations and results to devise and solve a mathematical equation describing the behavior of the electron in a hydrogen atom. The modern description of the electrons in atoms (the quantum model) came from the mathematical solutions to the Schrodinger equation.

Section 1: Revising the Atomic Model Like the Bohr model, the quantum mechanical model of the atom restricts the energy of electrons to certain values. Unlike the Bohr model, the quantum mechanical model does not specify an exact path the electron takes around the nucleus. The quantum mechanical model determines the allowed energies an electron can have and how likely it is to find the electron in various locations of an atom.

Section 1: Revising the Atomic Model In the quantum mechanical model of the atom, the probability of finding an electron within a certain volume of space surrounding the nucleus can be represented as a fuzzy cloud region. The cloud is more dense where the probability of finding the electron is high and is less dense there the probability of finding the electron is low. There is no boundary to the cloud because there is a slight chance of finding the electron at a considerable distance from the nucleus.

quantum mechanical model electron cloud model charge cloud model Schroedinger, Pauli, Heisenberg, Dirac (up to 1940): According to the QMM, we never know for certain where the e– are in an atom, but the equations of the QMM tell us the probability that we will find an electron at a certain distance from the nucleus.

Section 1: Revising the Atomic Model Atomic Orbitals Solutions to the Schrodinger equation give the energies, or energy levels, an electron can have. For each energy level, the Schrodinger equation also lead to a mathematical expression, called an atomic orbital, describing the probability of finding an electron at various locations around the nucleus. An atomic orbital is expressed pictorially as a region of space in which there is a high probability of finding an electron. (figure 5.4)

Section 1: Revising the Atomic Model The energy levels of electrons in the quantum mechanical model are labeled by principal quantum umbers (n). Each energy level corresponds to one or more orbitals of different shapes. n= 1, 2, 3, 4, and so forth. Indicates the main energy level (shell) occupied by the electron. As n increases, the electron’s energy and its average distance from the nucleus increases.

Section 1: Revising the Atomic Model If n = 1, the electron occupies the 1st (lowest) main energy level and is located closest to the nucleus. This is the ground state More than one electron can have the same n value. The numbers and types of atomic orbitals depend on the principal energy level. The total number of orbitals that exist in a given shell (main energy level) = n2.

Section 1: Revising the Atomic Model Angular Momentum Quantum Number (l) AKA Azimuthal Quantum Number Indicates the shape of the orbital (cloud). Describes the electrons density and cloud pattern. For a specific main energy level, the number of orbital shapes is = n.

Section 1: Revising the Atomic Model Values of l are 0 and all + integers < n-1. If n = 1 then l = 0 If n = 2 then l = 0, 1 If n = 3 then l = 0, 1, 2 If n = 4 then l = 0, 1, 2, 3

Section 1: Revising the Atomic Model Orbital letter designations according to values of l If l is 0 then the letter designation is s. If l is 1 then the letter designation is p. If l is 2 then the letter designation is d. If l is 3 then the letter designation is f.

Section 1: Revising the Atomic Model Orbital shapes s orbitals are spherical. p orbitals have dumbbell shapes. d orbitals have crossing double dumbbell shapes. f orbitals are too complex to discuss here.

Electron Configurations d orbital (double dumbell) s orbital (spherical) p orbital (dumbbell)

Section 1: Defining the Atom Possible sublevels 1st energy level (n=1) – only one sublevel possible (1-s orbital) 2nd energy level (n=2) – there are 2 sublevels (2-s and 2-p orbitals) 3rd energy level (n=3) – there are 3 sublevels (3-s, 3-p, and 3-d orbitals) 4th energy level (n=4) – there are 4 sublevels (4-s, 4-p, 4-d, and 4-f orbitals) Each atomic orbital is designated by the principal quantum number followed by the letter of the sublevel. 1s, 2s2p, 3s3p3d,…

Section 1: Revising the Atomic Model Magnetic Quantum Number (mi) Indicates the orientation of an orbital around the nucleus. Charges are in whole units. -l…-1,0,1…+l

Section 1: Revising the Atomic Model   l Orbital letter designation mI –l…-1,0,1…+l Number orbitals In sublevel (2l + 1) s 1 p -1,0,+1 3 2 d -2,-1,0,1,2 5 f -3,-2,-1,0,1,2,3 7

Section 1: Revising the Atomic Model Spin Quantum Number (ms) Indicates the direction of magnetic spin The fundamental spin states of an electron in an orbital. Only 2 possible values (+ ½ and – ½ ) A single orbital can hold a maximum of 2 electrons, which must have opposite spins.

Section 1: Revising the Atomic Model   l Orbital letter designation mI –l…-1,0,1…+l Number orbitals per sublevel (2l + 1) Number of electrons per sublevel 2(2l + 1) s 1 2 p -1,0,+1 3 6 d -2,-1,0,1,2 5 10 f -3,-2,-1,0,1,2,3 7 14