Hydrogen atom orbitals

One (n = 1)The p orbitals occupy the x, y and z axes and point at right angles to each other, so are oriented perpendicular to one anotherThe lobes of the p orbitals become larger and longer with increasing shell numberRepresentation of orbitals (the dot represents the nucleus of the atom) showing spherical s orbitals (a), p orbitals containing ‘lobes’ along the x, y and z axisNote that the shape of the d orbitals is not requiredAn overview of the shells, subshells and orbitals in an atomGround stateThe ground state is the most stable electronic configuration of an atom which has the lowest amount of energyThis is achieved by filling the subshells of energy with the lowest energy first (1s)The order of the subshells in terms of increasing energy does not follow a regular pattern at n = 3 and higherThe ground state of an atom is achieved by filling the lowest energy subshells firstElectron Arrangement SummaryEach shell can be divided further into subshells, labelled s, p, d and fEach subshell can hold a specific number of orbitals:s subshell : 1 orbitalp subshell : 3 orbitalsd subshell : 5 orbitalsf subshell : 7 orbitalsEach orbital can hold a maximum number of 2 electrons so the maximum number of electrons in each subshell are as follows:s : 1 x 2 = total of 2 electronsp : 3 x 2 = total of 6 electronsd : 5 x 2 = total of 10 electronsf : 7 x 2 = total of 14 electronsSummary of the Arrangement of Electrons in Atoms TableMain Energy Level (n)Sub ShellsNumber of orbitals in sub-shellTotal number of electrons in each orbitalTotal number of electrons in main shell1s1222s128p363s1218p36d5104s1232p36d510f714

First group elements (H and He) cannot have more than 2 electrons, since they have only 1s orbitals in their configurations.Second period elements (C,N,O,F) cannot have more than 8 electrons around the central atom. This is due to the lack of empty d orbitals and hence these elements can not have expanded octet.Elements from the third period onwards can have an expanded octet due to the introduction of d orbitals in these periods.3. H and F can never be the central atom as they need only one electron to complete their respective duplet and octet. These elements make only single bonds with other elements. STEP 3 : COMPLETE THE OCTET.COMPLETE THE OCTET OF THE MOST ELECTRONEGATIVE ATOM WITH MINIMUM FORMAL CHARGESFormal charge is the charge assigned to an atom in a molecule or ion on the basis of the difference in valence electrons and electrons used by the atom in the Lewis dot structure. It is defined as the valence electrons of the atom minus electrons used by atom in making bonds and as lone pairs. An atom is supposed to use all electrons of its valence shell, but if it uses more or less than the number of electrons in its valence shell, then it gets a formal charge. For every covalent bond, an atom gives one electron so number of bonds around each atom will give the number of electrons used in making covalent bonds. Similarly for every lone pair it uses a pair of electrons.Hence formal charge

ShellsThe arrangement of electrons in an atom is called the electron configurationElectrons are arranged around the nucleus in principal energy levels or principal quantum shellsPrincipal quantum numbers (n) are used to number the energy levels or quantum shellsThe lower the principal quantum number, the closer the shell is to the nucleusSo, the first shell which is the closest to the nucleus is n = 1The higher the principal quantum number, the greater the energy of the shell and the further away from the nucleusEach principal quantum number has a fixed number of electrons it can holdn = 1 : up to 2 electronsn = 2 : up to 8 electronsn = 3 : up to 18 electronsn = 4 : up to 32 electronsSubshellsThe principal quantum shells are split into subshells which are given the letters s, p and dElements with more than 57 electrons also have an f shellThe energy of the electrons in the subshells increases in the order s The order of subshells appears to overlap for the higher principal quantum shells as seen in the diagram below:Electrons are arranged in principal quantum shells, which are numbered by principal quantum numbersOrbitalsSubshells contain one or more atomic orbitalsOrbitals exist at specific energy levels and electrons can only be found at these specific levels, not in between themEach atomic orbital can be occupied by a maximum of two electronsThis means that the number of orbitals in each subshell is as follows:s : one orbital (1 x 2 = total of 2 electrons)p : three orbitals ( 3 x 2 = total of 6 electrons)d : five orbitals (5 x 2 = total of 10 electrons)f : seven orbitals (7 x 2 = total of 14 electrons)The orbitals have specific 3-D shapess orbital shapeThe s orbitals are sphericalThe size of the s orbitals increases with increasing shell numberE.g. the s orbital of the third quantum shell (n = 3) is bigger than the s orbital of the first quantum shell (n = 1)p orbital shapeThe p orbitals have a dumbbell shapeEvery shell has three p orbitals except for the first

Molecules. A molecule cannot have a permanent dipole moment if it a) has a center of inversion b) belongs to any of the D point groups c) belongs to the cubic groups T or OApplications of Group Theory 2. Predicting chirality of molecules. Chiral molecules lack an improper axis of rotation (Sn), a center of symmetry (i) or a mirror plane (σ).Applications of Group Theory 3. Predicting the orbitals used in σ bonds. Group theory can be used to predict which orbitals on a central atom can be mixed to create hybrid orbitals.Applications of Group Theory 4. Predicting the orbitals used in molecular orbitals. Molecular orbitals result from the combining or overlap of atomic orbitals, and they encompass the entire molecule.Applications of Group Theory 5. Determining the symmetry properties of all molecular motion (rotations, translations and vibrations). Group theory can be used to predict which molecular vibrations will be seen in the infrared or Raman spectra.Determining Hybridization 1. Determine the point group of the molecule. 2. Consider the σ bonds as vectors, and determine how they are transformed by the symmetry operations of the group. 3. Obtain the characters for the bonds. For each symmetry operation, a bond which remains in place contributes a value of +1. If the bond is moved to another position, it contributes a value of 0. 4. Reduce the set of characters to a linear combination of the character sets of the point group.Hybridization • Determine the hybridization of boron in BF3. The molecule is trigonal planar, and belongs to point group D3h. 1. Consider the σ bonds as vectors. Fa B Fc FbHybridization • Determine the hybridization of boron in BF3. The molecule is trigonal planar, and belongs to point group D3h. 1. Consider the σ bonds as vectors. Fa B Fc FbHybridization Determine

Staircase: not only are the stair steps set at specific heights but the height between steps is fixed). Finally, Bohr suggested that the energy of light emitted from electrified hydrogen gas was equal to the energy difference of the electron’s energy states:Elight = hν = ΔEelectronThis means that only certain frequencies (and thus, certain wavelengths) of light are emitted. Figure 8.5 “Bohr’s Model of the Hydrogen Atom” shows a model of the hydrogen atom based on Bohr’s ideas.Figure 8.5 Bohr’s Model of the Hydrogen AtomBohr’s description of the hydrogen atom had specific orbits for the electron, which had quantized energies.Bohr’s ideas were useful but were applied only to the hydrogen atom. However, later researchers generalized Bohr’s ideas into a new theory called quantum mechanics, which explains the behaviour of electrons as if they were acting as a wave, not as particles. Quantum mechanics predicts two major things: quantized energies for electrons of all atoms (not just hydrogen) and an organization of electrons within atoms. Electrons are no longer thought of as being randomly distributed around a nucleus or restricted to certain orbits (in that regard, Bohr was wrong). Instead, electrons are collected into groups and subgroups that explain much about the chemical behaviour of the atom.In the quantum-mechanical model of an atom, the state of an electron is described by four quantum numbers, not just the one predicted by Bohr. The first quantum number is called the principal quantum number. Represented by n. (n). The principal quantum number largely determines the energy of an electron. Electrons in the same atom that have the same principal quantum number are said to occupy an electron shell of the atom. The principal quantum number can be any nonzero positive integer: 1, 2, 3, 4,….Within a shell, there may be multiple possible values of the next quantum number, the angular momentum quantum number. Represented by ℓ. (ℓ). The ℓ quantum number has a minor effect on the energy of the electron but also affects the spatial distribution of the electron in three-dimensional space—that is, the shape of an electron’s distribution in space. The value of the ℓ quantum number can be any integer between 0 and n − 1:ℓ = 0, 1, 2,…, n − 1Thus, for a given value of n, there are different possible values of ℓ:If n equalsℓ can be1020 or 130, 1, or 240, 1, 2, or 3and so forth. Electrons within a shell that have the same value of ℓ are said to occupy a subshell in the atom. Commonly, instead of referring to the numerical value of ℓ, a letter represents the value of ℓ (to help distinguish it from the principal quantum number):If ℓ equalsThe letter is0s1p2d3fThe