The Magnetic Quantum Number 2

Summary of Bohr’s Model (1913) Electrons orbit the nucleus with different orbits at different fixed distances from the nucleus. (1) Electrons that leave one orbit must move to another orbit. (2) Electrons only change orbits if specific amounts (quanta) of extra energy from the outside world are involved. (3) Electrons that receive enough extra energy from the outside world can leave the atom they are in. (4) Electrons that return to orbits they used to reside in give up the extra energy they acquired when they moved in the first place. (5) Electronic energy given up when electrons move back into an original orbit often show up as a specific color light. (6)

One Quantum Number Bohr Atom Model 1 2 3 n the principal quantum number Electrons in these atoms are defined only by the principle quantum number. Two Quantum Number Bohr Atom Model 1,0 2,0 2,1 n the principal quantum number l the angular momentum (azimuthal) quantum number

Two Quantum Number Bohr Atom Model 1,0 2,0 2,1 Two Quantum Number Bohr Atom Model This superscript tells us how many electrons are in the orbit. 2 2 3 1s 2s 2p Two quick questions! (1) What is the 2 quantum number Bohr atom short hand notation for the ground state (the lowest energy arrangement) electron configuration of the carbon atom? (Remember that the carbon atom has 6 protons.) 2 2 2 1s 2s 2p (2) What about the helium atom? (The helium atom has 2 protons.) 2 1s

Three Quantum Number Bohr Atom Model 1,0 2,0 2,1 Three Quantum Number Bohr Atom Model A Bohr atom model that uses two quantum numbers explain the spectra for many more atoms. What happened when a third quantum number was added to the model?

Three Quantum Number Bohr Atom Model 1,0 2,0 2,1 Three Quantum Number Bohr Atom Model n the principal quantum number l the angular momentum (azimuthal) quantum number 1,0,0 2,0,0 2,1,-1 2,1, 0 2,1, 1 m the magnetic quantum number The third quantum number is called the magnetic quantum number.

Three Quantum Number Bohr Atom Model 1,0,0 2,0,0 2,1,-1 2,1, 0 2,1, 1 Three Quantum Number Bohr Atom Model the principal quantum number the angular momentum (azimuthal) quantum number n l the magnetic quantum number m This seems messy and complicated but it really is not! To help make things easier: a short hand “nickname” orbit (energy level) naming system was created.

Three Quantum Number Bohr Atom Model 1,0,0 2,0,0 2,1,-1 2,1, 0 2,1, 1 Three Quantum Number Bohr Atom Model the principal quantum number the angular momentum (azimuthal) quantum number n l the magnetic quantum number m Use nitrogen as an example. First, list the energy levels (orbits) for the three quantum number Bohr model for the nitrogen atom. 1, 0, 0 2, 0, 0 2, 1, -1 How many electrons does a Nitrogen atom (atomic number 7) have? 2, 1, 0 2, 1,+1 Answer: seven

Three Quantum Number Bohr Atom Model 1,0,0 2,0,0 2,1,-1 2,1, 0 2,1, 1 Three Quantum Number Bohr Atom Model the principal quantum number the angular momentum (azimuthal) quantum number n l the magnetic quantum number m Second, arrange these 5 energy terms (levels) horizontally. 1,0,0 2,0,0 2,1,-1 2,1,0 2,1,+1 Third, when necessary, use a subscript letter to identify the magnetic quantum number, as illustrated by the three 2p orbitals below. 1s,0 2s,0 2p x 2p y 2p z

Three Quantum Number Bohr Atom Model 1,0,0 2,0,0 2,1,-1 2,1, 0 2,1, 1 Three Quantum Number Bohr Atom Model 1,0,0 2,0,0 2,1,-1 2,1,0 2,1,+1 or 1s,0 2s,0 2p x 2p y 2p z Fourth, as before, show the number of electrons in each energy level (orbit) as a superscript number. 2 2 1 1 1 1s,0 2s,0 2p x 2p y 2p z

Three Quantum Number Bohr Atom Model 1,0,0 2,0,0 2,1,-1 2,1, 0 2,1, 1 Three Quantum Number Bohr Atom Model 2 2 1 1 1 1s,0 2s,0 2p x 2p y 2p z Finally, Remove (but remember) the 0 magnetic quantum number value associated with any “s” energy level and separate each energy term by a comma. 2 2 1 1 1 1s , 2s , 2p x , 2p y , 2p z

Three Quantum Number Bohr Atom Model 1,0,0 2,0,0 2,1,-1 2,1, 0 2,1, 1 1s 2s 2p y x z Three Quantum Number Bohr Atom Model the principal quantum number the angular momentum (azimuthal) quantum number n l the magnetic quantum number m The 5 lowest energy terms (orbits) in the three quantum number Bohr atom mode are 1s , 2s , 2p x , 2p y , 2p z

Three Quantum Number Bohr Atom Model 1s 2s 2p y x z 1s 2s 2p y x Three Quantum Number Bohr Atom Model Two quick review questions. (1) What are the 5 lowest energy terms (orbits) for nitrogen? 2 1s , 2 2s , 1 2p x , 2p y 1 , 2p z 1 (2) What are the names of the lowest energy terms (orbits) for a carbon atom. (Remember that carbon’s atomic number is 6) 1s 2 , 2s 2 , 2p x 1 , 2p y 1 The carbon atom has 6 protons and 6 electrons.

Four Quantum Number Bohr Atom Model 1s 2s 2p x 2p y The three quantum number atom model was very successful explaining various light energies observed in the spectra of atoms. 2p z However, in some cases, there were definite spectra lines that were clearly different colors but very close together. A fourth and final quantum number was added to the Bohr model to account for these light waves that differed by only a small amount of energy. The spin quantum number

Summary of the Three Quantum Number Bohr Atom Model Electrons returning to their “ground” state can emit light with a unique frequency (energy). Atoms in the ground state are filled with electrons from the orbit closest to the nucleus to the orbit furthest from the nucleus. The diagonal fill rule predicts the electron configuration of an atom’s ground state. The magnetic quantum number identifies two electrons within an atom as a group.