Question

Given that the electron configuration for phosphorus is \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{3},\) answer the following questions: a. How many electrons are in each atom? b. What is the atomic number of this element? c. Write the orbital notation for this element. d. How many unpaired electrons does an atom of phosphorus have? e. What is its highest occupied energy level? f. How many inner-shell electrons does the atom contain? g. In which orbital(s) are these inner-shell electrons located?

Short answer

a. 15 electronsb. Atomic number is 15c. 1s: ↑↓ 2s: ↑↓ 2p: ↑↓ ↑↓ ↑↓ 3s: ↑↓ 3p: ↑ ↑ ↑d. 3 unpaired electronse. Highest occupied energy level is 3f. 10 inner-shell electronsg. Located in 1s, 2s, and 2p orbitals.

Step-by-step solution

Determine the number of electrons

Count the total number of electrons in the given electron configuration: 1s^2 2s^2 2p^6 3s^2 3p^3Adding these, the total number of electrons is 2 (1s) + 2 (2s) + 6 (2p) + 2 (3s) + 3 (3p) = 15.

Find the atomic number

The atomic number is equal to the number of electrons in a neutral atom. From step 1, the total number of electrons is 15, so the atomic number of phosphorus is 15.

Write the orbital notation

The orbital notation can be written using the given electron configuration. Each level or subshell is represented by a box or a line with arrows indicating the spin of electrons. For phosphorus, the notation is:1s: ↑↓2s: ↑↓2p: ↑↓ ↑↓ ↑↓3s: ↑↓3p: ↑ ↑ ↑

Determine the number of unpaired electrons

Examine the 3p subshell in the orbital notation. There are three electrons in the 3p subshell, and they each occupy separate orbitals to minimize repulsion. Hence, phosphorus has three unpaired electrons in the 3p subshell: 3.

Identify the highest occupied energy level

The highest occupied energy level in the given electron configuration is the third energy level (3s and 3p), so the highest occupied energy level is 3.

Count the inner-shell electrons

Inner-shell electrons are those not in the outermost energy level. For phosphorus, the outermost energy level is the third. The inner-shell electrons include all electrons in the 1s, 2s, and 2p orbitals:Inner-shell electrons = 2 (1s) + 2 (2s) + 6 (2p) = 10.

Locate the inner-shell electrons

The inner-shell electrons are located in the 1s, 2s, and 2p orbitals, based on the calculated inner-shell electrons from step 6.

Key concepts

atomic number

The atomic number of an element is crucial for identifying it. It tells us the number of protons in the nucleus of an atom. For a neutral atom, it also equals the number of electrons. Using phosphorus as an example, its electron configuration is given as \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{3}\). By counting the total electrons, we get:

• 2 electrons in 1s,
• 2 in 2s,
• 6 in 2p,
• 2 in 3s,
• 3 in 3p.

Adding them gives a total of 15 electrons. Hence, the atomic number of phosphorus is 15. This atomic number directly correlates to the element's identity.

orbital notation

Orbital notation provides a visual representation of the distribution of electrons in an atom across its various sublevels and orbitals. For phosphorus with an electron configuration of \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{3}\), the orbital notation helps us visualize how electrons fill up their respective orbitals:

• 1s: ↑↓
• 2s: ↑↓
• 2p: ↑↓ ↑↓ ↑↓
• 3s: ↑↓
• 3p: ↑ ↑ ↑

In this notation:

• Each box or line shows an orbital,
• Arrows represent the electrons,
• The direction of each arrow denotes the electron's spin.

This specific notation shows how phosphorus's electrons are arranged in increasing energy levels.

unpaired electrons

Unpaired electrons are those electrons which are alone in an orbital and do not have a paired counterpart with an opposite spin. In orbital notation, these are represented by single arrows (↑) in a box. For the phosphorus atom, looking at the 3p subshell we see three single electrons:

• 3p: ↑ ↑ ↑

Here, each p orbital (there are three of them: \(3 p_{x}\), \(3 p_{y}\), and \(3 p_{z}\) ) has one unpaired electron. Therefore, in phosphorus, there are three unpaired electrons. These unpaired electrons are crucial in determining some chemical properties of the element, such as its magnetism.

highest occupied energy level

The highest occupied energy level in an atom is the one that contains electrons with the most energy. It corresponds to the principal quantum number 'n' of the highest filled electron shell. For phosphorus, with an electron configuration of \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{3}\), the highest occupied energy level is '3', containing the 3s and 3p orbitals.

• The 3s sublevel has 2 electrons.
• The 3p sublevel has 3 electrons.

This tells us that the third energy level has 5 electrons in total, which are the outermost or valence electrons of the phosphorus atom. Valence electrons are key in determining how an atom interacts and bonds with other atoms.

inner-shell electrons

Inner-shell electrons are those electrons that are not in the outermost or highest energy level. These electrons reside in the lower shells and do not usually participate in chemical bonding. In the case of phosphorus, with the electron configuration \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{3}\), the inner-shell electrons are located in the 1s, 2s, and 2p orbitals. Calculating the total number:

• 1s: 2 electrons
• 2s: 2 electrons
• 2p: 6 electrons

Summing these gives 10 inner-shell electrons. These inner-shell electrons help to shield the outer electrons from the nucleus, affecting properties such as ionization energy and atomic size.