QUANTUM NUMBERS

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  • QUANTUM NUMBERS
    • The set of numbers used to describe the position and energy of the electron in an atom.

    • There are four quantum numbers:
    1. Principal quantum number
    2. Azimuthal quantum number
    3. Magnetic quantum number
    4. Electron spin quantum number
    • The first three (n, l, ml) specify the particular orbital of interest or describe the size, shape, and orientation in space of the orbitals on an atom.
    • The fourth (ms) specifies how many electrons can occupy that orbital.
    • ORBITAL (Atomic Orbital) – a wave function for an electron in an atom; a region of space in which there is a high probability of finding the electron; a three-dimensional description of the most likely location of an electron around an atom.
  • Principal Quantum Numbers (n)
    • It describes the main energy level (MEL) on which the orbital resides.
    • It designates the principal electron shell of the atom.
    • It describes the general distance of an electron from the nucleus
    • The farther the electron from the nucleus, the higher is the energy; a larger value of the principal quantum number implies a greater distance between the electron and the nucleus – in turn, implies a greater atomic size.
    • It largely determines the energy of an atom.
    • It can be any nonzero positive integer: 1, 2, 3, 4…
    • It can be any integer with a positive value that is equal to or greater than one. 
    • It cannot have a negative value or be equal to zero because it is not possible for an atom to have a negative value or no value for a principal shell.
    • Example:
    • If n=7, what is the principal electron shell?
    • Answer: Since n refers to the principal energy level/ or energy shell, so if n=7 then the principal energy shell =7.
  • Azimuthal Quantum Numbers (l) OR Orbital Angular Momentum Quantum Number (l)
    • It describes the shape of a given orbital.
    • It describes the subshell/sub-energy level (SEL) where the electron is.
    • Allowed values of l are integers ranging from 0 to n−1. Thus, for a given value of n, there are different possible values of l.
  • Other term for azimuthal quantum numbers?
    orbital angular momentum quantum number
  • Azimuthal quantum numbers
    A) 1
    B) 0 or 1
    C) 3
    D) 0 1 2 or 3
    • Commonly, instead of referring to the numerical value of l, a letter represents the value of l (to help distinguish it from the principal quantum number).
    • It affects the spatial distribution of the electron in three-dimensional space; that is, the shape of the electron’s distribution in space.
  • Azimuthal quantum number
    NOTE: 0 TO N-1
    A) SHARP
    B) PRINCIPAL
    C) DIFFUSE
    D) FUNDAMENTAL
    • Example: 
    • If n=3, the azimuthal quantum number can take on the following values – 0,1, and 2. 
    • When l=0, the resulting subshell is an ‘s’ subshell. 
    • When l=1 and l=2, the resulting subshells are ‘p’ and ‘d’ subshells (respectively). 
    • When n=3, the three possible subshells are 3s, 3p, and 3d.
    • If n=7, what are the possible values of l?
    • Answer: Since l can be zero or a positive integer less than (n-1), it can have a value of 0, 1, 2,3,4,5, or 6.
  • Magnetic Quantum Numbers (ml)
    • It describes the three-dimensional orientation of an electron’s distribution in space.
    • The value of the magnetic quantum number is dependent on the value of the azimuthal (or orbital angular momentum) quantum number. 
    • For a given value of l, the value of ml ranges between the interval -l to +l.
    • Therefore, in any given energy level, there can be up to 1s orbital, 3p orbitals, 5d orbitals, 7f orbitals, and so forth.
  • Magnetic quantum number
    • NOTE: -l to +l
    A) 0
    B) -1 0 1
    • The value of ml dictates the orientation of an electron’s distribution in space. 
    • When l = zero, ml can be only zero, so there is only one possible orientation. 
    • When l = 1, there are three possible orientations for an electron’s distribution. 
    • When l = 2, there are five possible orientations of electron distribution. 
    • This goes on and on for other values of l, but we need not consider any higher values of l here. Each value of ml designates a certain orbital. Thus, 
    • there is only one orbital when l is zero, 
    • three orbitals when l is 1, 
    • five orbitals when l is 2, and so forth.
  • Spin Quantum Numbers (ms)
    • It specifies the orientation of the spin axis of an electron.
    • The electron spin quantum number is independent of the values of n, l, and ml.
    • The positive value of ms implies an upward spin on the electron which is also called ‘spin up’ and is denoted by the symbol ↑. 
    • If ms has a negative value, the electron in question is said to have a downward spin, or a ‘spin down’, which is given by the symbol ↓.
    • The possible values are +½ and -½.
    • Example:
    • Can an electron with ms = ½ have a downward spin?
    • Answer: No, if the value of ms is positive, the electron is “spin up”.
    1. valid
    2. invalid
    3. valid
    4. invalid
    5. valid
    6. valid
    7. invalid
    8. valid
    9. valid
    10. invalid
  • Determining Spin Quantum Numbers
    • How do electrons enter orbitals? 
    • Electrons singly occupy orbitals first and then they pair up, as shown in the following illustration. 
    • Each box represents one orbital, and an orbital can only have a maximum number of two electrons. 
    • There are three 'p' orbitals, and on the left side, it is shown how the 'p' orbitals are filled. 
    • There are five 'd' orbitals, and on the right side, it is shown how 'd' orbitals are filled as the number of electrons increases.
  • Spin quantum numbers
  • Paramagnetism and Diamagnetism
    • The spin of an electron makes it behave like a small magnet, in that the spin determines the magnetic property of an atom.
    • Magnetism is the behavior of a substance when exposed to a magnetic field that is related to the presence of paired and unpaired electrons in the material.
    • It can be predicted using an orbital diagram.
    • An atom with unpaired electrons are termed as paramagnetic
    • results in a net magnetic field because electrons within the orbital are not stabilized or balanced enough
    • atoms are attracted to magnets
    -
    • An atom with paired electrons are termed as diamagnetic
    • results in no magnetic field because electrons are uniform and stabilized within the orbital
    • atoms are not attracted to magnets
  • Assigning Spin Direction
    • Restrictions apply when assigning spin directions to electrons.
    • When one is filling an orbital, such as the p orbital, you must fill all orbitals possible with one electron spin before assigning the opposite spin. 
    1. Pauli Exclusion Principle
    • Declares that there can only be a maximum of two electrons for every one orientation, and the two electrons must be opposite in spin direction; meaning one electron has ms = +1/2 and the other electron has ms = −1/2 .
  • 2. Hund's Rule
    • Declares that the electrons in the orbital are filled up first by the upward spin (+1/2  spin). Once all the orbitals are filled with unpaired +1/2  spins, the orbitals are then filled with the -1/2 spin.
  • read and analyze
    Identifying Spin Direction
    1. Determine the number of electrons the atom has.
    2. Draw the electron configuration for the atom. 
    3. Distribute the electrons, using up and down arrows to represent the electron spin direction.