• All elements in existence are made up of tiny particles called atoms
• Each of these atoms are made of subatomic particles called protons, electrons, and neutrons
• The Relative Atomic Mass is used to describe the masses of these subatomic particles, because they are too small to compare their masses with conventional means.
• The relative atomic mass of an element is the number of times the average mass of one atom of the element is heavier than one-twelfth of the mass of one atom of carbon-12.
• Relative atomic mass = average mass of one atom of the element ÷ ¹/_12^th of the mass of 1 atom of carbon-12
• The relative atomic mass of Hydrogen is 1, which means 12 atoms of hydrogen would have exactly the same mass as 1 atom of carbon
• The relative atomic mass has no units

Isotopes

• Isotopes are atoms of the same element that have the same atomic numbers but different mass numbers
• The Atomic Number (or Proton Number) is the number of protons (or electrons) in the nucleus of an atom
• The Mass Number (or Nucleon Number) is the sum of the number of protons and neutrons in an atom
• Protons and neutrons can be collectively called nucleons
• Therefore, isotopes are atoms of the same element which posses the same number of protons (or electrons) but have different number of neutrons.

• Some examples of isotopes include:
  

 

• Isotopes are divided into Radioactive and Non-radioactive
• Non-radioactive isotopes are stable atoms while non-radioactive isotopes are unstable atoms due to the imbalance of neutrons and protons, which causes the nucleus to decay over time through nuclear fission and emit radiation.
• Example of radioactive isotopes include, cobalt-60, tritium.
• These radioactive isotopes can be used medically and industrially:
  • Cobalt-60 is frequently used to kill cancerous cells
  • Sterilization of medical instruments and materials
  • Radioactive dating; using carbon-14 to date carbon-containing materials, such as organic matter, etc.
  • As fuel for nuclear power plants, etc

Electronic Structure

• Electrons move very fast around the nucleus of an atom
• They move in orbital paths called shells
• The electronic structure of an atom can be represented using diagrams (electronic shell diagrams) or by writing out its electronic configuration
• Using electronic shell diagram:
  • Electrons move around the nucleus in shells (energy levels)
  • Each of these shells has a different amount of energy associated with it
  • The shell closest to the nucleus can hold only 2 electrons, the second, 8 electrons, and the third, 18 electrons, and so on.
  • At the point when a shell becomes full – it contains the maximum amount of electrons it can hold – the electrons begin to fill the next shell.
  • The further away from the nucleus, the more energy the shell has.
  • An atom becomes stable if and when it completely fills its outermost shell with the maximum amount of electrons it can hold.
    
• Using Electronic Configuration:
  • The electronic structure can be translated into numbers
  • The number of notations depict the period of the element in the periodic table
  • The last notation depicts the group of the element in the periodic table
  • The electronic configuration of chlorine is 2,8,7; it has 3 notations, hence it is period 3; it’s last notation is 7, hence it is group 7.

Quantum Numbers

• The electronic configuration can also be expressed using quantum numbers.
• Every electron in an atom has a set of four quantum numbers unique to it
• These numbers are:
  • Principal Quantum Number, n
  • Angular Momentum (Azimuthal Quantum Number), l
  • Magnetic Quantum Number, m_l
  • Spin Quantum Number, m_s

Principal Quantum Number

• This number always takes integer values, 1, 2, 3, etc.
• The values of n represent the energy levels or main shells of an atom, and also indicate their relative distances from the nucleus. For example n = 1 represents the first energy level which is nearest to the nucleus.
• The maximum number of electrons in a given main shell ‘n’ is equal to 2n². For example, n = 2 would have a maximum number of electrons equal to 8.
• The value of n for a given level is equal to the number of sub-shells or sub-levels in the energy level. For example, n = 3 indicates that the 3^rd energy level is made up of three sub-levels or sub-shells.

Angular Momentum Quantum Number

• This quantum number always takes values of 0 to n – 1 for a given value of n.
• If n = 3, l would be 0, 1, 2
• Sub-levels are often designated by small letters s, p, d, f which correspond to the angular momentum 0, 1, 2, 3, ..
• The number of l values for a given shell n is equal to the number of sub-shells in that main shell (energy level). For example, in the 3^rd main shell, where n = 3, there are three sub-levels:
  • l = 0 (s sub-level)
  • l = 1 (p sub-level)
  • l = 2 (d sub-level)
• The energy of sub-levels increases as the value of l increases

Magnetic Quantum Number

• This quantum number always takes values of -1 to +1 for a given value of l. i.e. m_l = -l to +l
• If n = 1, l = 0, therefore, m = 0. Therefore, the s sub-level in the first energy level gives rise to only one m value
• If n = 2, l = 0, 1; for l = 0, m = 0; for l = 1, m = -1, 0, +1. Thus, the p sub-level gives rise to three m values.
• The number of m values obtained from a given l value is equal to the number of orbitals within the sub-shell or sub-level. Thus, the:
  • s sub-level (l = 0) has only one s orbital
  • p sub-level (l = 1) has three p orbitals
• The magnetic quantum number describes the direction that the orbital projects in space and each value of m indicates a specific orientation for the orbital it represents.
• For the p sub-level (l = 1), m values of -1, 0, +1 correspond to three equivalent orbitals p_x, p_y, and p_z which are orientated along the x, y, and z axes respectively.
• The number of identical orbitals in a given sub-level is given by m = 2l + 1
• Thus, as shown above, the number of equivalent orbitals in the :
  • s sub-level (l = 0) is 1
  • p sub-level (l = 1) is 3
  • d sub-level (l = 2) is 5
  • f sub-level (l = 3) is 7
• An orbital is a charge cloud distribution for electrons within a sub-level. It is a region in space where the probability of finding electrons is high
• Orbitals with the same l value have the same shape.
• The s-orbitals are spherical in shape while the p orbitals have a dumb-bell shape
  

  Photo Credit: Study.com

Spin Quantum Number

• This quantum number describes the orbital motion of an electron on its own axis.
• It takes a value of +¹/₂ for clockwise motion and a value of –¹/₂ for anticlockwise
• There are no two electrons in an orbital of an atom with the same spin quantum number
• In all cases, if the spin quantum number for one of the electrons is +¹/₂, the second must have –¹/₂.

Capacity of Sub-shells and Orbitals

• In an atom, a shell or main energy level refers to all orbitals with the same principal quantum number, n.
• All shells, except the first shell, are divided into sub-shells
• A sub-shell is a group of orbitals with the same principal quantum number and the same angular momentum quantum number
• The number of sub-shells in a shell is the same as the principal quantum number of the shell
• The first shell can hold a maximum of two electrons which must go into the 1s sub-shell or orbital. This implies that the only sub-shell or orbital in the first energy level (n = 1), designated 1s, can hold a maximum of two electrons.
• The second shell (n = 2), which consists of s and p sub-shells, can hold a maximum of 8 electrons. If the s sub-shell (or 2s sub-shell) takes its maximum of two electrons, then the p sub-shell (or 2p sub-shell) must hold a maximum of six electrons
• The third shell (n = 3), which consists of s, p, and d sub-shells can hold a maximum of 18 electrons. If the s, and p sub-shells (or 3s and 3p sub-shells) take their maximum of 2 and 6 electrons, respectively, then the d sub-shell (or 3d sub-shell) must hold a maximum of 10 electrons
• The fourth shell (n = 4), which consists of s, p, d, and f sub-shells, can hold a maximum of 32 electrons. If the 4s, 4p, and 4d sub-shells take their maximum of 2, 6, and 10 electrons respectively, then the 4f orbital would hold a maximum of 14 electrons.
  
• A movement from tail to head along each arrow from top to bottom gives an arrangement of sub-shells in order of increasing energy or decreasing stability
  
• Magnetic quantum number values show that the p, d, and f sub-shells comprise of 3, 5, and 7 orbitals respectively. Each of these orbitals can hold a maximum of 2 electrons
• Thus, the p sub-shell in the second shell may be written as 2p⁶ or 2p_x² 2p_y² 2p_z²

Examples

1. Using the quantum numbers, write out the electronic configuration for the following elements
   1. Chlorine
      • The atomic number of Cl is 17
      • Fill each sub-shell with the maximum amount of electrons they can hold: 1s² 2s² 2p⁶ 3s² 3p⁵
   2. Sodium
      • The atomic number of Na is 11
      • Fill each sub-shell with the maximum amount of electrons they can hold: 1s² 2s² 2p⁶ 3s¹
   3. Nitrogen
      • The atomic number of N is 7
      • Fill each sub-shell with the maximum amount of electrons they can hold: 1s² 2s² 2p³
   4. Calcium
      • The atomic number of Ca is 20
      • Fill each sub-shell with the maximum amount of electrons they can hold: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s²

Rules for Writing Electronic Structures

• Electronic configuration (or electronic structure) is the orderly distribution of electrons into shells, sub-shells, and orbitals of an atom.
• There are three rules which govern the distribution of electrons into shells and orbitals of atoms. These rules include:

1. Aufbau’s Principle:
   • When filling electrons into atoms, electrons occupy the lowest-energy orbitals first before going into higher energy orbitals.
   • The sequence of filling the energy levels of orbitals follows the order given above:
     
   • Using this principle:
     • ₆C = 1s² 2s² 2p²
     • ₁₉K = 1s² 2s² 2p⁶ 3s² 3p⁶ 4s¹
     • ₃₀Zn = 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰
2. Hund’s Rule:
   • This rule states that each of the orbitals in a set of orbitals of equal energy must be filled by an electron before a second electron enters any of them
   • Using this rule:
     • ₆C = 1s² 2s² 2p_x¹ 2p_y¹ 2p_z⁰ NOT 1s² 2s² 2p_x² 2p_y⁰ 2p_z⁰
     • ₇N = 1s² 2s² 2p_x¹ 2p_y¹ 2p_z¹ NOT 1s² 2s² 2p_x² 2p_y¹ 2p_z⁰
3. Pauli Exclusion Principle:
   • This principle states that no two electrons in any atom have the same set of four quantum numbers, therefore, no two electrons in the same orbital have the same spin quantum number
   • This is often illustrated using boxes for orbitals and arrows for electrons.
   • An arrow pointing upwards indicates an electron with a +½ spin quantum number while an arrow pointing downwards indicates an electron with a -½ spin quantum number.
   • Using this rule:
     

     Photo Credit: Chemistry Score