Question

Following the laws of quantum Mechanics: Calculate the number of orbitals and number of electrons in different kinds of orbitals for n = 5 to 9. Explain what two electrons are allowed per orbital, and calculate the number of orbitals and total number of electrons for a given n. Does the calculation indicate a Pi or Sigma bond? Would this these natural atomic orbitals have an overlap?

Answer 1

As per quantum mechanics, n represents the energy level. For each energy level, there are n² orbitals and each orbital can hold upto two electrons, hence 2n² electrons.

For n=5, Number of orbitals = 5²=25 and  Number of electrons= 2*5²=50

For n=6, Number of orbitals = 6²=36 and  Number of electrons= 2*6²= 72

For n=7, Number of orbitals = 7²=49 and  Number of electrons= 2*7²= 98

For n=6, Number of orbitals = 8²= 64 and  Number of electrons= 2*8²= 128

For n=6, Number of orbitals = 9²=81 and  Number of electrons= 2*9²= 162

The reason why only two electrons can occupy an orbital at a time is because as per Pauli's exclusion principle, no two electrons can have all four quantum numbers as same. Now electrons in same orbital will have first three quantum numbers same and differ only by spin quantum number which at a time can be different only for two electrons. Hence among the two electrons, one will have a positive spin and the other has negative spin. Howevr we cannot define the sigma or Pi bonding as perthese calculations. Within an atom, the degenerate subshells (of same energy level) may overlap.