06_ Electronic Structure of an Atom.pptx

Chemistry

1. QUANTUM MECHANICAL DESCRIPTION OF ATOM SCHRÖDINGER’S MODEL OF HYDROGEN ATOM AND WAVE FUNCTIONS MAIN ENERGY LEVELS, SUBLEVELS, AND ORBITALS QUANTUM NUMBERS ELECTRON CONFIGURATION Chemistry for Industrial Technologist

2. Atoms are the basic units of matter and the defining structure of elements. The term comes from the Greek word atomos , or indivisible, because it was once thought that atoms were the smallest things in the universe and could not be divided . Atoms are made up of three particles: protons, neutrons, and electrons — which are composed of even smaller particles, such as quarks .

3. COASTLINE PARADOX SUPERPOSITION

4. A body at will remain at , and a body in motion will remain in motion unless it is acted upon by an external force. The net force acting on an object is equal to the of that object times its acceleration. (Hint: F=ma) For every action, there is an equal and opposite . The pull of gravity between two objects will be to the masses of the objects and inversely to the square of the distance between their centers of mass. (Hint: It starts with p) Energy cannot be nor destroyed, and instead changes from one form to another. In the absence of external forces such as friction, when objects collide, the total momentum before the collision is the as the total momentum after the collision. (Hint: Equivalent, similar) Within a continuous streamline of fluid flow, a fluid's hydrostatic pressure will balance in contrast to its speed and elevation.

5. A body at rest will remain at rest , and a body in motion will remain in motion unless it is acted upon by an external force. The net force acting on an object is equal to the mass of that object times its acceleration. For every action, there is an equal and opposite reaction . The pull of gravity between two objects will be proportional to the masses of the objects and inversely proportional to the square of the distance between their centers of mass. Energy cannot be created nor destroyed, and instead changes from one form to another. In the absence of external forces such as friction, when objects collide, the total momentum before the collision is the same as the total momentum after the collision. Within a continuous streamline of fluid flow, a fluid's hydrostatic pressure will balance in contrast to its speed and elevation. Newton’s First Law of Motion Newton’s Second Law of Motion Newton’s Third Law of Motion Newton’s Law of Universal Gravitation Law of Conservation of Energy Law of Conservation of Momentum Bernoulli’s Principle These are some of the laws and principles that govern .

6. Quantum mechanics is the science that deals with the behavior of matter and light on atomic and subatomic scale . It results in what may appear to be some very strange conclusions about the physical world. At the scale of atoms and electrons, many of the equations of classical mechanics cease to be useful . In classical mechanics, objects exist in a specific place at a specific time. In quantum mechanics, however, objects exist in a haze of probability . Quantum mechanics seeks to understand the laws governing the nature, behavior, and interactions of matter and energy at very small scales and energies.

7. In 1924, Louis de Broglie hypothesized that atomic particles, such as electrons, have wavelike behaviors . Electrons do not behave like particles flying through space. That meant that, in general, we cannot describe their exact paths . In 1927, Werner Heisenberg showed that it is impossible to take any measurement of an object without disturbing it. The Heisenberg Uncertainty Principle states that it is fundamentally impossible to know precisely both the velocity and position of a particle at the same time . The only quantity that can be known is the probability for an electron to occupy a certain region around the nucleus. In 1926, Erwin Schrödinger proposed a new atomic model called the Quantum Mechanical Model (or the so- called Electron Cloud Model), in which electrons are treated as waves. Unlike Bohr’s atomic model (1913), the Schrödinger equation can be applied equally to elements other than hydrogen .

8. Summary Atoms are made up of protons, neutrons, and electrons, which, in turn, are composed of quarks. Atoms are the basic units of matter. Comes from the word atomos , meaning "indivisible". Quantum mechanics seeks to understand the laws governing the nature, behavior, and interactions of atomic and subatomic particles.

9. SCHRÖDINGER’S MODEL OF HYDROGEN ATOM AND WAVE FUNCTIONS

10. John Dalton (1803) J. J. Thomson (1904) Ernest Rutherford (1911) Niels Bohr (1913) Billiard Ball Model Plum Pudding Model Planetary Model Bohr Model

11. Quantum Mechanical Model Erwin Schrödinger (1926) In this model, electrons were no longer depicted as particles moving around a central nucleus in a fixed orbit. Instead, Schrodinger proposed a model whereby scientists could only make educated guesses as to the positions of electrons. Hence, their locations could only be described as being part of a “cloud” around the nucleus where the electrons are likely to be found .

12. Quantum Mechanical Model Erwin Schrödinger (1926) In this model, electrons were no longer depicted as particles moving around a central nucleus in a fixed orbit. Instead, Schrodinger proposed a model whereby scientists could only make educated guesses as to the positions of electrons. Hence, their locations could only be described as being part of a “cloud” around the nucleus where the electrons are likely to be found . Electron Cloud Model The Quantum Mechanical (or Electron Cloud) Model differs from the Bohr Model in that it does not define the exact path of an electron.

13. In 1926, Erwin Schrödinger reasoned that if electrons behave as waves , then it should be possible to describe them using a wave equation. A wave function is defined to be a function describing the probability of a particle's quantum state as a function of position, momentum, time, and/or spin. Wave functions are commonly denoted by the variable Ψ . Every electron has an associated wave function, and the wave function tells you everything there is to know about the electron.

14. Wave functions are used in formulating the Schrödinger equation. Schrödinger equation describes the form of the probability waves that govern the motion of small particles. Schrödinger established the correctness of the equation by applying it to the hydrogen atom , predicting many of its properties with remarkable accuracy. The form of the Schrödinger equation depends on the physical situation. The most general form is the time- dependent Schrödinger equation description of a system evolving with time. (above), which gives a i – imaginary unit ħ – Planck’s constant Ѱ – wave function H or Ĥ – Hamiltonian operator

15. Summary A wave function is defined as the probability of a particle's position, momentum, time, and/or spin. The Quantum Mechanical Model depicts electrons as waves moving in an electron cloud. That means their locations are defined in terms of their most likely position inside an atom. The Schrödinger equation describes the form of probability waves that govern the motion of small particles.

16. Electron orbits around the nucleus are called energy levels . Levels are definite stable energies that a quantum mechanical particle can have. According to quantum theory, only certain energy levels are possible. Main levels are numbered from 1, 2, 3, 4, and so on, with the 1st level being the orbit closest to the nucleus. These main energy levels can be broken down into sublevels . Sublevels are comprised of sharp ( s ), principal ( p ), diffuse , and fundamental ( f ) orbitals. 1st level has 1 sublevel (s). 2nd level has 2 sublevels (s, p). 3rd level has 3 sublevels (s, p, d). 4th level has 4 sublevels (s, p, d, f).

17. Orbitals are spaces which have high probability of finding an electron. In other words, an orbital is an area where electrons live. Orbitals also refer to the mathematical function that describes the wave- like behavior of electrons in an atom. Orbitals are located and are part of energy sublevels . Each orbital can be occupied by a maximum of two electrons , each with its own electron spin. Electron spin has a value of ± ½, which depends with its orientation. If the electron spins clockwise on its axis, it is described as spin- up or +½. Else, If the electron spins counterclockwise , it is described as spin- down or - ½.

18. 1 s 1 2 2 s, p 4 (1+3) 8 (2+6) 3 s, p, d 9 (1+3+5) 18 (2+6+10) 4 s, p, d, f 16 (1+3+5+7) 32 (2+6+10+14)

19. Summary Levels are definite stable energies that a quantum mechanical particle can have. Main levels are numbered from 1, 2, 3, 4, and so on, with the 1st being the orbit closest to the nucleus. Main energy levels can be broken down into sublevels. Sublevels are comprised of sharp (s), principal (p), diffuse (d), and fundamental (f) orbitals. Orbitals are spaces with high probability of finding an electron. Each orbital are occupied by two electrons, each with its own electron spin (+½ or - ½).

20. A quantum number is a value that is used when describing the energy levels available to atomic and subatomic particles. An electron has four quantum numbers to describe its state and yield solutions to the Schrödinger equation: Principal quantum number (n) describes the energy level of electrons. Angular momentum quantum number (ℓ) describes the energy sublevel. Magnetic quantum number (m ℓ or m) describes the orbital of the sublevel. Spin quantum number (m s or s) describes the spin of an electron.

21. The principal quantum number can have integral values 1, 2, 3, and so on. In a hydrogen atom, the value of n determines the energy of an orbital. Although, this is not the case for many electron atoms. The principal quantum number also describes the size of the orbital. Orbitals for which n = 2 are larger than those for which n = 1, for example. The larger the size of the orbital, the greater the distance of the electron from the nucleus. Principal quantum number (n) describes the energy level of electrons.

22. The angular momentum quantum number tells us the shape of the orbital (i.e., spherical, polar, cloverleaf, or complex). For a given value of n, ℓ has possible integral values in the form n ≤ 1. If n = 1, then ℓ = 0. If n = 2, then ℓ = and 1. If n = 3, then ℓ = 0, 1, and 2. The value of ℓ is generally designated by letters . ℓ = 0 is called sharp or s ℓ = 1 is called diffuse or d ℓ = 2 is called principal or p ℓ = 3 is called fundamental or f After f, orbital designations follow alphabetical order (g, h, i, k, ...). Angular momentum quantum number (ℓ) describes the energy sublevel.

23. A collection of orbitals with the same value n is called shell , while orbitals with the same n and ℓ values are referred to as subshell . For example, the shell with n = 2 is composed of two subshells, ℓ = and 1. These subshells are called 2s and 2p , where 2 denotes the value of n , and s and p denote the values of ℓ .

24. The magnetic quantum number designates the orientation of the orbital in space. For a given value of ℓ, m ℓ has possible integral values in the form -ℓ ≤ m ℓ ≤ ℓ. If ℓ = 0, then m ℓ = 0. If ℓ = 1, then m ℓ = -1, and 1. If ℓ = 2, then m ℓ = -2, -1, 0, 1, and 2. Magnetic quantum number (m ℓ ) describes the orbital of the sublevel.

25. ℓ ℓ 1 (s) 1s 1 1s 2 2 0, 1 (s, p) - 1, 0, 1 2s 1 2s 2 2p 1 2p 2 2p 3 2p 4 2p 5 2p 6 3 0, 1, 2 (s, p, d) - 1, 0, 1 - 2, - 1, 0, 1, 2 3s 1 3s 2 3p 1 3p 2 3p 3 3p 4 3p 5 3p 6 3d 1 3d 2 3d 3 3d 4 3d 5 3d 6 3d 7 3d 8 3d 9 3d 10 4 0, 1, 2, 3 (s, p, d, f) - 1, 0, 1 - 2, - 1, 0, 1, 2 - 3, - 2, - 1, 0, 1, 2, 3 4s 1- 2 4p 1- 6 4d 1- 10 4f 1 4f 2 4f 3 4f 4 4f 5 4f 6 4f 7 4f 8 4f 9 4f 10 4f 11 4f 12 4f 13 4f 14

26. According to the electromagnetic theory, a spinning charge generates a magnetic field . If electrons are thought of as spinning on their own axes, their magnetic properties can be announced for. To take the electron spin into account, it is necessary to introduce a fourth quantum number , called the spin quantum number. Spin quantum number suggests that electrons behave as if they were spinning either clockwise or counterclockwise . Electrons in an orbital are arbitrarily assigned with m s of either +½ or -½, depending on how it is observed. Spin quantum number (m s ) describes the spin of an electron.

27. ℓ ℓ 1s 1 1 (s) ±½ 2p 2 2 1 (p) - 1, 0, 1 ±½ 3d 4 3 2 (d) - 2, - 1, 0, 1, 2 ±½ 4f 6 4 3 (f) - 3, - 2, - 1, 0, 1, 2, 3 ±½

28. Summary A quantum number is a value that is used to describe the energy levels available to atomic and subatomic particles. Four quantum numbers are used describe distribution of electrons in an atom: principal (n), angular momentum (ℓ), magnetic (m ℓ ), and spin (m s ). n describes the size of the orbital. ℓ tells the shape of the orbital. m ℓ defines the orientation of the orbital. m s assigns the spin of electrons inside an orbital.

29. Electron configuration is the distribution of electrons of an atom or molecule in atomic or molecular orbitals. It describes each electrons as moving independently in an orbital, in an average field created by all other orbitals. The electron configuration chart is a tabular representation of patterns in the electron configuration as one goes down the periodic table of elements. According to the laws of quantum mechanics, electrons can move from one configuration to another through emission or absorption of photons . Mathematically, configurations are described by Slater determinants or configuration state functions.

30. Orbital diagrams show the arrangement of electrons in orbitals within an atom. Boxes are used to represent orbitals. Single arrow (↑) represents 1 electron. Double arrows (↑↓) represent 2 electrons. Orbital diagram for Hydrogen. 1s

31. Orbital diagrams show the arrangement of electrons in orbitals within an atom. Boxes are used to represent orbitals. Single arrow (↑) represents 1 electron. Double arrows (↑↓) represent 2 electrons. Orbital diagram for Carbon. 1s 2s 2p

32. Orbital diagrams show the arrangement of electrons in orbitals within an atom. Boxes are used to represent orbitals. Single arrow (↑) represents 1 electron. Double arrows (↑↓) represent 2 electrons. Orbital diagram for Nitrogen. 1s 2s 2p

33. Pauli Exclusion Principle states that, in an atom or molecule, no two electrons can have the same four quantum numbers. Because an orbital only contains two electrons, the two electrons must have opposing spins . It was proposed by Austrian physicist Wolfgang Pauli in 1925 to describe the behavior of electrons. As a consequence, subshells have certain electron arrangement that corresponds to the electron configuration in which orbitals are written.

34. Hund's rule states that: Every orbital in a sublevel is singly-occupied before any orbital is doubly-occupied. All of the electrons in singly- occupied orbitals have the same spin, as to maximize the total spin. When assigning electrons to orbitals, an electron first seeks to fill all the orbitals with similar energy (also referred to as degenerate orbitals) before pairing with another electron in a half- filled orbital. Electrons always enter an empty orbital before they pair up. Atoms at ground states tend to have as many unpaired electrons as possible .

35. The Aufbau Principle, simply put, means electrons are added to orbitals as protons are added to an atom. Lower electron orbitals fill before higher orbitals do , "building up" the electron shell. The end result is that the atom, ion, or molecule forms the most stable electron configuration . The term comes from the German word Aufbau , meaning “built up” or “construction”. Aufbau Principle outlines the rules used to determine how electrons are organized into shells and subshells . It is also known as the building- up principle or the Aufbau Rule . Like most rules, there are also exceptions to the rule. Half- filled and completely- filled d and f subshells add stability to the atoms, so the d and f block elements don't always follow the principle.

36. Any time two electrons share the same orbital, their spin quantum numbers have to be different . One of the electrons has to be spin- up , while the other electron has to be spin- down . Whenever two electrons are paired together in an orbital, or their total spin is 0, they are called diamagnetic electrons . Since electrons in the same orbital always have opposite values for spin quantum number, they will always end up cancelling each other out. Diamagnetic atoms are not attracted to a magnetic field , but are rather slightly repelled.

37. Electrons that are alone in an orbital are called paramagnetic electrons . If an electron has no pair, the orbital has a net spin , because the spin of the lone electron does not get cancelled out. An atom is considered to be paramagnetic when it contains at least one paramagnetic electron. In other words, an atom could have as many paired electrons, but as long as it also has an unpaired electron , it is still considered a paramagnetic atom. Paramagnetic properties are due to the realignment of the electron paths caused by the external magnetic field.