Enter the total number of electrons and the total number of orbitals into the calculator to determine the electron distribution in an atom’s orbitals and sublevels according to Hund’s Rule.

Hund’s Rule Formula

The following formula is used to calculate the electron distribution in an atom’s orbitals and sublevels according to Hund’s Rule. 

ED = (e / o) + (e (p) o)

Variables:

  • ED is the electron distribution in an atom’s orbitals and sublevels
  • e is the total number of electrons in the atom
  • o is the total number of orbitals in the atom’s sublevel
  • % is the modulus operator, which gives the remainder of the division of e by o

To calculate the electron distribution, divide the total number of electrons by the total number of orbitals. This gives the number of orbitals that will be fully occupied. The remainder of this division (e % o) gives the number of orbitals that will be half occupied. The sum of these two numbers gives the total electron distribution according to Hund’s Rule.

What is a Hund’s Rule?

Hund’s Rule is a principle in quantum mechanics that states that electrons will occupy an empty orbital before they pair up in an already occupied one. This rule is used to explain the distribution of electrons in an atom’s orbitals and sublevels, helping to predict an atom’s magnetic properties. It is based on the idea that electrons in the same orbital with the same spin create a more stable arrangement, minimizing electron-electron repulsion.

How to Calculate Hund’s Rule?

The following steps outline how to calculate the Hund’s Rule using the given formula:

  1. First, determine the total number of electrons in the atom (e).
  2. Next, determine the total number of orbitals in the atom’s sublevel (o).
  3. Next, calculate the division of e by o.
  4. Then, calculate the remainder of the division of e by o using the modulus operator (%).
  5. Finally, add the results of the division and the modulus calculation to get the electron distribution in the atom’s orbitals and sublevels (ED).

Example Problem:

Use the following variables as an example problem to test your knowledge:

Total number of electrons in the atom (e) = 24

Total number of orbitals in the atom’s sublevel (o) = 4