Wednesday October 24, 2012

1. WednesdayOctober 24, 2012 • (Main and Sub-Energy Levels, Orbitals; Aufbau, Hund, and Pauli; Quantum Numbers; • WS – Arrangement of Electrons in Atoms)

2. Bell RingerWednesday, 10-24-12 • Write the • isotopic notation • electron configuration notation • Lewis Dot Structure • for the following atoms: Be, B, N, F, Mg, Al, Ca, Br

3. Announcements

5. Main Energy Levels An atom can have up to 7 main energy levels, which we have called “lanes of the track.” These correspond to the 7 periods of the Periodic Table.

6. Energy Sub-Levels The main energy levels can further divided into sublevels, which we call s, p, d, and f. Energy level 1 – s-sublevel only Energy level 2 – s- and p-sublevels Energy level 3 – s-, p-, and d-sublevels Energy level 4 – s-, p-, d-, and f-sublevels Energy level 5 – s-, p-, d-, and f-sublevels Energy level 6 – s-, p-, and d-sublevels Energy level 7 – s-sublevel only (so far) Remember that s-sublevels can hold up to 2 electrons, p-sublevels up to 6 electrons, d-sublevels up to 10 electrons, and f-sublevels up to 14 electrons.

7. Orbitals An orbital is like a shoebox with electrons being the shoes. An electron “orbital” can hold only 2 electrons, regardless of the energy sublevel it is in. Since an s-sublevel can only hold 2 electrons, it can contain only 1 orbital. A p-sublevel can hold 6 electrons, so it can contain 3 orbitals. A d-sublevel can hold 10 electrons, so it can contain 5 orbitals. An f-sublevel can hold 14 electrons, so it can contain 7 orbitals.

8. Rules for Electron Insertion into the Electron Cloud These three laws must be followed by electrons in orbitals of an atomic cloud. The Aufbau Principle Hund’s Rule The Pauli Exclusion Principle

9. The Aufbau Principle An electron occupies the lowest energy orbital that can receive it Example The 4s orbital is filled before the 3d

10. Hund’s Rule Orbitals of equal energy are each occupied by one electron before any orbital is occupied by a second electron, and all electrons in singly occupied orbitals must have the same spin. _____ _____ _____ 2px 2py 2pz

11. A school bus after a rainstorm Hund’s Rule Orbitals of equal energy are each occupied by one electron before any orbital is occupied by a second electron, and all electrons in singly occupied orbitals must have the same spin. All students will try to get their own seat on a separate row until all rows are filled with one student. Only then will they begin to double-up.

12. The Pauli Exclusion Principle No two electrons in the same atom can have the same set of four quantum numbers. Electrons occur in pairs with opposite spins.

13. The Principle Quantum Number The principal quantum number (n)indicates the main energy level occupied by the electron. Values of n are positive integers only - 1, 2, 3, and so on. As n increases, the electron’s energy and its average distance from the nucleus increase. For example, an electron for which n = 1 occupies the first, or lowest, main energy level and is located closest to the nucleus. As you will see, more than one electron can have the same n value, and these electrons are sometimes said to be in the same electron shell. The total number of orbitals that exist in a given shell, or main energy level, is equal to n2.

14. The Angular Momentum Quantum Number The angular momentum quantum number, (l), indicates the shape of the orbital. Except at the first main energy level, orbitals of different shapes (known as sublevels) exist for a given value of n. For a specific main energy level, the number of orbital shapes possible is equal to n. The values of l allowed are zero and all positive integers less than or equal to n − 1. For example, orbitals for which n = 2 can have one of two shapes corresponding to l = 0 and l = 1

15. The Angular Momentum Quantum Number Depending on its value of l, an orbital is assigned a letter. s orbitals are spherical, p orbitals have dumbbell shapes, and d orbitals are more complex. (The f orbital shapes are too complex to discuss here.) In the first energy level, n = 1, there is only one sublevel possible - an s orbital. As mentioned, the second energy level, n = 2, has two sublevels - the s and p orbitals. The third energy level, n = 3, has three sublevels - the s, p, and d orbitals. The fourth energy level, n = 4, has four sublevels - the s, p, d, and f orbitals. In an nth main energy level, there are n sublevels

16. The Angular Momentum Quantum Number Each atomic orbital is designated by the principal quantum number followed by the letter of the sublevel. For example, the 1s sublevel is the s orbital in the first main energy level, while the 2p sublevel is the set of p orbitals in the second main energy level. On the other hand, a 4d orbital is part of the d sublevel in the fourth main energy level. How would you designate the p sublevel in the third main energy level? How many other sublevels are in the same main energy level with this one?

17. The Magnetic Quantum Number The magnetic quantum number, (m), indicates the orientation of an orbital around the nucleus. Atomic orbitals can have the same shape but different orientations around the nucleus. Here we describe the orbital orientations that correspond to various values of m. Because an s orbital is spherical and is centered around the nucleus, it has only one possible orientation. This orientation corresponds to a magnetic quantum number of m = 0. There is therefore only one s orbital in each s sublevel. s-orbitals: m = 0

18. The Magnetic Quantum Number The lobes of a p orbital can extend along the x, y, or z axis of a three-dimensional coordinate system. There are therefore three p orbitals in each p sublevel, which are designated as px, py , and pz orbitals. The three p orbitals occupy different regions of space and correspond, in no particular order, to values of m = −1, m = 0, and m = +1 so far. p-orbitals: m = -1, m = 0, m = +1

19. There are five different d orbitals in each d sublevel. The five different orientations, including one with a different shape, correspond to values of m = −2, m = −1, m = 0, m = +1, and m = +2 The Magnetic Quantum Number

20. There are seven different f orbitals in each f sublevel. The total number of orbitals at a main energy level increases with the value of n. In fact, the number of orbitals at each main energy level equals the square of the principal quantum number, n2. What is the total number of orbitals in the third energy level? Specify each of the sublevels using the three quantum numbers you’ve learned so far. The Magnetic Quantum Number

21. Like Earth, an electron in an orbital can be thought of as spinning on an internal axis. It spins in one of two possible directions, or states. As it spins, it creates a magnetic field. To account for the magnetic properties of the electron, theoreticians of the early twentieth century created the spin quantum number. The spin quantum number has only two possible values (+1/2 , −1/2) which indicate the two fundamental spin states of an electron in an orbital. A single orbital can hold a maximum of two electrons, which must have opposite spins. The Spin Quantum Number

22. Arrangement of Electrons in Atoms Worksheet