Chapter 15, Problem 1RCQ

How many electrons can occupy the first shell? How many can occupy the second shell?

To determine

The number of electrons that can occupy first shell and second shell.

Answer to Problem 1RCQ

Solution:

Two electrons can occupy the first shell and eight electrons can occupy the second shell.

Explanation of Solution

In structure of Atom, electrons are found inside the shells. The shells represents the primary energy levels of an atom. Each shell has a set of sub-shells which represents various energy levels of the shells. Each sub-shell (except s-subshell) has further divided on the basis of energy levels – which are called “orbitals”.

Quantum numbers illustrates the possible energy levels and sub-energy levels of an atom. The four types of quantum numbers are – Principal quantum number, Angular quantum number, Magnetic quantum number and Spin quantum number.

Principal quantum number correlates to the possible number of shells in an atom. It is designated as ‘n’. The shells are represented as numerical positive integers 1, 2, 3, etc or alphabetically – K, L, M, N etc.

Angular quantum number gives the energy levels within the shell – which is also known as sub-shells. It also represents the shape of the sub-shells. Accordingly K-shell has only one sub-shell termed as‘s’. L-subshell has 2 sub-shells that are‘s’ and ‘p’. M-shell has 3 sub-shells that are termed as‘s’, ‘p’ and‘d’ and so on.

Magnetic quantum number explains about the possible energy levels of the sub-shells. They are called “orbitals”.

Spin quantum number represents the spin of the electron that occupy in the orbital.

According to Aufbau’s principle, electrons are occupied from the lowest energy level to highest energy level.

According to Hund’s rule, electrons are singly occupied in all the orbitals of the sub-shells and all those electrons have parallel spin. After the electrons are singly occupied, electrons further occupy the singly filled orbitals with opposite spin. This relates to Pauli’s exclusion principle which states an orbital can have only two electrons which must have opposite spins with respect to each other.

Each orbital can accommodate two electrons of opposite spins. The first shell has one s-orbital and 2 electrons are occupied in it. The second shell has 2 sub-shells – s and p. Six electrons are occupied in the 3 p-orbitals as two electrons per p-orbital. Further the p-subshell also has an s-orbital and 2 electrons can be occupied there. Totally 8 electrons can occupy the second shell.

Conclusion:

The number of electrons that can occupy first shell and second shell have been determined