Quantum Numbers PDF

QUANTUM NUMBERS  LEARNING COMPETENCIES The learners should be able to: ✓Use quantum numbers to describe an electron in an atom; STEM_GC11ESIIa-b-54 ✓Determine the magnetic property of the atom based on its electronic configuration; STEM_GC11ESIIa-b-57 ✓Draw an orbital diagram to represen...

QUANTUM NUMBERS  LEARNING COMPETENCIES The learners should be able to: ✓Use quantum numbers to describe an electron in an atom; STEM_GC11ESIIa-b-54 ✓Determine the magnetic property of the atom based on its electronic configuration; STEM_GC11ESIIa-b-57 ✓Draw an orbital diagram to represent the electronic configuration of atoms. STEM_GC11ESIIa-b-58  LEARNING OBJECTIVES A.Describe the four quantum numbers and use it to describe an electron in an atom. B.Identify if an element is para magnetic or diamagnetic based on its electronic configuration. C.Draw an orbital diagram to represent the electronic configuration of atoms. Heisenberg’s Uncertainty Principle states that it is impossible that both the energy and position of an electron can be known at the same time. Thus, as we know more about the electron’s energy, we know less about its position, and vice versa. Bohr’s Model of the hydrogen atom suggest that the electron orbits the nucleus like our solar system. However, the Quantum Mechanical description of the hydrogen atom has proven that the Bohr’s model of electron is incorrect. Quantum Mechanical states that we don’t know exactly where the electron is, but with high probability, we can conclude that the electron is most likely to be found in an orbital. In this lesson, you should be able to describe the electrons in orbitals using the 4 quantum numbers.  What is QUANTUM NUMBERS? QUANTUM NUMBERS are values that describe specific properties of electrons in an atom. They help to determine the location, energy, and behavior of an electron determine the location, energy, and behavior of an electron within the atom.  QUANTUM NUMBERS All electrons have four quantum numbers which describe the location of electrons in the electron cloud of an atom and can be used to determine the electron configuration of an atom. According to the Pauli Exclusion Principle, each electron in an atom has an exclusive set of quantum numbers and no two electrons can have the same combination of four quantum numbers. THE QUANTUM NUMBERS QUANTUM NUMBER SYMBOL POSSIBLE VALUES 1, 2, 3, 4…. (positive Principal Quantum Number n integers) Azimuthal/ Angular 0, 1, 2, 3…. (0 to n-1) Momentum Quantum Number ℓ Magnetic Quantum Number 𝑚𝑙 -ℓ,….-1,0,1….,+ℓ Electron Spin Quantum 𝑚𝑠 +1/2, -1/2 Number  PRINCIPAL QUANTUM NUMBER (n) describes the energy level or shell an electron occupies. It also determines the distance of the electron from the nucleus. Higher values of n means the electron is further from the nucleus and has more energy. It may take the values of any possible integer: 1, 2, 3, 4, and so on. Shell refers to a group of electrons that orbit the nucleus of an atom at a certain distance, corresponding to a specific energy level. PRINCIPAL QUANTUM NUMBER (n) n Shell 1 K 2 L 3 M 4 N Note: K is closest to the nucleus and has the lowest energy Role of the Shell Number: ✓ Distance from the Nucleus: The larger the principal quantum number n, the farther the electron is from the nucleus. ✓ Energy Level: Electrons in higher-numbered shells (larger n) have more energy than those in lower-numbered shells. ✓ Capacity: The maximum number of electrons in a shell is given by the formula 2𝒏𝟐. For example: n = 1 (first shell) can hold up to 2 electrons. n = 2 (second shell) can hold up to 8 electrons. n = 3 (third shell) can hold up to 18 electrons. The principal quantum number n is crucial for determining the size, energy, and electron capacity of each shell in an atom. FOR EXAMPLE: What is the n of Sodium? 1𝒔𝟐 2 𝒔𝟐 2 𝒑𝟔 3 𝒔𝟏 Determining n: The electrons in the 1s orbital have n=1. The electrons in the 2s and 2p orbitals have n=2. The electron in the 3s orbital has n=3. Summary: The highest principal quantum number (n) for sodium is 3, as the outermost electron is in the 3s orbital. LET’S PRACTICE! Find the Principal Quantum Number (n) of the following: 1) Carbon 2) Helium 3) Sulfur 4) Nickel 5) Magnessium LET’S PRACTICE! Find the Principal Quantum Number (n) of the following: 1) Carbon - 2 2) Helium - 1 3) Sulfur - 3 4) Nickel - 4 5) Magnessium - 3  AZIMUTHAL QUANTUM NUMBER (l) also known as Angular Momentum Quantum Number. defines the shape of the electron's orbital (the region where the electron is most likely found). It can take values from 0 to n−1, representing different orbital shapes (s, p, d, f). Describes the shape of an electron's orbital within an atom. It determines the type of subshell (s, p, d, f) the electron occupies. NAME SUB- TOTAL NO. OF AZIMUTHAL OF SUB- SHAPE SHELL ELECTRONS SHELL 0 s Sharp 2 Spherical 1 p Principal 6 Dumbbell 2 d Diffused 10 Clover 3 f Fundamental 14 Complex VALUES OF l BASED ON n: When: n =1, l can only be 0 (this is the s orbital). n=2, l can be 0 or 1 (representing s and p orbitals). n=3, l can be 0, 1, or 2 (representing s, p, and d orbitals). n=4, l can be 0, 1, 2, or 3 (representing s, p, d, and f orbitals). FOR EXAMPLE: What is the l of Sodium? 1𝒔𝟐 2 𝒔𝟐 2 𝒑𝟔 3 𝒔𝟏 Determining the l: 1s Orbital: Electrons: 2, n = 1, l = 0 (s orbital) 2s Orbital: Electrons: 2, n = 2, l = 0 (s orbital) 2p Orbitals: Electrons: 6, n = 2, l = 1 (p orbital) 3s Orbital: Electrons: 1, n = 3, l = 0 (s orbital) The angular momentum quantum number (l) for sodium: The maximum l value in sodium is 1 (from the 2p orbitals). The outermost electron is in the 3s orbital, where l=0. LET’S PRACTICE! Find the Azimuthal Quantum Number (l) of the following: 1) Carbon - 2) Helium - 3) Sulfur - 4) Nickel - 5) Magnessium - LET’S PRACTICE! Find the Azimuthal Quantum Number (l) of the following: 1) Carbon – 1 2) Helium - 0 3) Sulfur - 1 4) Nickel - 2 5) Magnessium - 0  MAGNETIC QUANTUM NUMBER (𝒎𝒍 ) Describes the spatial orientation of an electron in a space or magnetic field. The value of 𝑚𝑙 depends on the value of l and may range from -1 to +1 including 0.  MAGNETIC QUANTUM NUMBER (𝒎𝒍 ) Orbital split up into degenerate orbitals (having same energy and size) in a magnetic field. Each degenerate orbital can hold up to 2 electrons. MAGNETIC QUANTUM NUMBER (𝒎𝒍 )  MAGNETIC QUANTUM NUMBER (𝒎𝒍 ) Degenerate AZIMUTHAL (𝒎𝒍 ) No. of Electrons Orbitals 0, s 0 1 2 1, p -1, 0, +1 3 6 2, d -2, -1, 0, +1, +2 5 10 -3, -2, -1, 0, +1, +2, 3, f +3 7 14 What is the Magnetic Quantum Number (𝒎𝒏 ) of Sodium? 1𝒔 2 𝒔 2𝒑 3𝒔 𝟐 𝟐 𝟔 𝟏 Determining the 𝒎𝒏 for Sodium: 1.The 3s orbital has an azimuthal quantum number l=0 (corresponds to s orbitals). 2.For l=0 (s orbital), 𝒎𝒏 can only be 0. Conclusion: The magnetic quantum number (𝒎𝒏 ) for Sodium (Na), with its outermost electron in the 3s orbital, is 0. LET’S PRACTICE! Find the Magnetic Quantum Number (𝒎𝒏 ) of the following: 1) Carbon - 2) Helium - 3) Sulfur - 4) Nickel - 5) Magnessium - LET’S PRACTICE! Find the Magnetic Quantum Number (𝒎𝒏 ) of the following: 1) Carbon - -1, 0 2)Helium - 0 3) Sulfur - -1, 0, +1 4) Nickel - -2, -1, 0, +1, +2 5) Magnessium - 0  ELECTRON SPIN QUANTUM NUMBER (𝒎𝒔 ) Indicates the direction of the electron’s spin which can be either up or down (+½ or -½). Example: What is the Electron Spin Quantum Number (𝒎𝒔 ) of Sodium? 1𝒔 2 𝒔 2 𝒑 3 𝒔 𝟐 𝟐 𝟔 𝟏 Since there is only one electron in the 3s orbital, it will have one of the two possible spins. The Electron Spin Quantum Number (𝒎𝒔 ) of the valence electron in Sodium is +1/2. LET’S PRACTICE! Find the Electron Spin Quantum Number (𝒎𝒔 ) of the following: 1) Carbon - 2) Helium - 3) Sulfur - 4) Nickel - 5) Magnessium - LET’S PRACTICE! Find the Electron Spin Quantum Number (𝒎𝒔 ) of the following: 1) Carbon - -1/2 2) Helium - -1/2 3) Sulfur - -1/2 4) Nickel - -1/2 5) Magnessium - -1/2  PARAMAGNETIC It refers to the magnetic state of an atom with one or more unpaired electrons. The unpaired electrons are attracted by a magnetic field due to the electrons’ magnetic dipole moments.  DIAMAGNETIC Substances are characterized by paired electrons. There is no net magnetic moment. The atom cannot be attracted into a magnet field. W PRACTICE EXERCISES Are you ready?  LAST ELECTRON Magnetic ELEMENT FROM THE n l 𝒎𝒍 𝒎𝒔 Property CONFIGURATION Calcium Potassium Boron Oxygen Neon W END OF PRESENTATION