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Quantum Numbers *Read Through the Lesson Notes. You Can Write Advanced Higher Chemistry CfE Unit 1 Inorganic Chemistry Lesson 4: Quantum Numbers *Read through the lesson notes. You can write them out, print them or save them. *Once you have tried to understand the lesson answer the questions that follow at the end. *The answers to the question sheet(s) will be posted later and this will allow you to self-evaluate your learning. Learning Intentions -Learn about the four quantum numbers used to describe electrons in an atom. -Learn about the Pauli exclusion principle. -Learn about the aufbau principle. -Learn about Hund’s rule. Background -Leading on from the lesson on spectroscopy, we discover that structure of the atom is more complex from that model which we have used since National 5 Chemistry. Evidence from emission spectra suggest that energy levels/shells of an atom consist of subshells. By obtaining emission spectra of greater resolution it is evident that what originally appeared to be one line is in fact two lines. Low resolution emission spectrum, showing one single line suggesting a transition of an electron between two definite energy levels. Quantum mechanics considers electrons as standing (stationary) waves as well as particles. An electron can only possess certain fixed amounts of energy known as quanta. There are different sizes and shapes of standing wave possible around the nucleus, known as atomic orbitals. The energy of the electron can be defined in terms of 4 quantum numbers. 1 Advanced Higher Chemistry CfE Unit 1 Inorganic Chemistry n: The principal quantum number, n, indicates the main energy level for an electron and is related to the size of the orbital. l: The angular momentum quantum number, l, determines the shape of the orbital. ml: The magnetic quantum number, ml , determines the orientation of the orbital. ms: The spin magnetic quantum number, ms, determines the direction of spin of the electron. 1. Principal Quantum Number, n Electrons are arranged in shells and are assigned a number, n, e.g. n= 1 1st shell n= 2 2nd shell n= 3 3rd shell …and so on The lower the value of n, the closer the shell is to the nucleus of the atom. Evidence from emission spectra indicates that these shells are subdivided into subshells. The subshells are described using the letters, s, p, d and f. The subshells are more commonly referred to as orbitals. The table below illustrates some of the subshells that are present in the first 4 shells. Shell Subshells First 1s Second 2s,2p Third 3s,3p,3d fourth 4s,4p,4d,4f 2. Angular Momentum Quantum Number, l This describes the shape of the orbital in which the electron is likely to be found. An s orbital is spherical and gets larger in size as n, the principal quantum number increases. 1s 2s 3s 2 Advanced Higher Chemistry CfE Unit 1 Inorganic Chemistry The maximum number of electrons in an orbital is two. Each s orbital can hold two electron. There are three types of p orbitals. They have the shape similar to a “figure of 8” and lie along the line of the axes, x, y and z. This gives them the names, Px, Py and Pz. The three p orbitals are described as “degenerate”, this means they are of equal energy. Each p orbital can hold a maximum of two electrons. There are five types of d orbitals (there is NO need to draw the d-orbitals, however, you are expected to be able to identify them). The five d orbitals are degenerate and each d orbital can hold a maximum of two electrons. *The shapes of the f orbitals are complex and are not required for this course. 3 Advanced Higher Chemistry CfE Unit 1 Inorganic Chemistry 3. Magnetic Quantum Number, ml This describes the spatial orientation of each orbital. 4. Spin Quantum Number, ms Quantum mechanics considers electrons spinning in one of two directions. * Later on in this unit, we will consider in greater detail the specific values of the four quantum numbers; n, l, ml and ms. To gain a better understanding of the way in which electrons are arranged in an atom, three concepts are useful. (i) The Pauli Exclusion Principle The Pauli exclusion principle states that no two electrons in an atom can have the same four quantum numbers. Therefore, when two electrons are present in one orbital they will adopt opposite spins. *A common way to represent electrons in an orbital is by using arrows. This diagram is commonly used to illustrate electrons in an orbital. 1s In this specific example, the arrows are showing two different electrons spinning in opposite directions. This means their spin quantum number values, ms, will be different. (ii) The Aufbau Principle The aufbau principle (coming from the German word to mean “building up”) says that electrons fill orbitals in order of increasing energy. It is important to note that the 4s orbital has lower energy than the 3d orbital and therefore is filled before. 4 Advanced Higher Chemistry CfE Unit 1 Inorganic Chemistry (iii) Hund’s Rule Hund’s rule states that, when degenerate orbitals are available, electrons fill singly and with parallel spins, before pairing up. p orbitals p orbitals This example shows the In this example, the fourth electrons filling single and electron has to share an with parallel spins orbital. Note that as the electron shares the orbital with another electron, they adopt opposite spins. Additional Resources -Watch the clips on Youtube: Crash course chemistry #25 (3 minutes- 5 minutes 30 seconds). https://www.youtube.com/watch?v=cPDptc0wUYI Crash course chemistry #5 (2 minutes 30 seconds- 6 minutes). https://www.youtube.com/watch?v=rcKilE9CdaA -Read Scholar Sections 2.1, 2.4 and 2.6 (some of the information will be covered later). Read the textbook BrightRed pages 12-14. -Answer the Question from Sheet 1.6 and check the answers when you have completed them. -If there are any questions regarding this lesson or the questions from sheet 1.6 then please leave a post on Microsoft Teams. 5 Advanced Higher Chemistry CfE Unit 1 Inorganic Chemistry 1.6 Orbitals 1. Later in this unit, we learn to represent the electronic configuration of an oxygen atom in the following way: *The single headed arrows represent electrons. (a) Use a similar representation to show (i) a lithium atom (ii) a beryllium atom (iii) a carbon atom (b) (i) State Hund’s Rule of Maximum Multiplicity. (ii) Show how the diagrammatic representation above for oxygen illustrates Hund’s Rule. (c) (i) State the Pauli Exclusion Principle. (ii) Show how the diagrammatic representation above for oxygen illustrates Pauli’s Principle. (d) (i) State the aufbau Principle. (ii) Show how the diagrammatic representation above for oxygen illustrates the aufbau Principle. (e) The three 2p orbitals are degenerate (i) Explain what is meant by degenerate. (ii) Name the three 2p orbitals. (iii) Draw diagrams which show the 3 dimensional arrangement of the three 2p orbitals. 2. a) Which quantum number describes the shape of an orbital? b) What does the quantum number ms describe? c) What does the magnetic quantum number describe? d) What is the maximum number of electrons that can occupy an orbital? e) i) If an electron is found in an orbital in the third energy level, what value would be given to the quantum number, n? ii) What is the maximum number of electrons that can be occupied by all five 3 d- orbitals? f) Which type of orbital is illustrated by the diagram below? 6 .
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