Electronic Structure: Number of Electrons: Study with Video Lessons, Practice Problems & Examples

An atom has electron shells, each with a maximum capacity determined by the formula $2^{\left(n\right)^2}$. For the first shell (n=1), it holds 2 electrons, while the second shell (n=2) can hold 8 electrons. Understanding these limits is crucial for grasping atomic structure and electron configuration, which are foundational concepts in chemistry.

Electronic Structure: Number of Electrons Concept 1

Now remember, an atom possesses shells. Each shell for a given atom has a maximum number of electrons it can hold. So here, when only the shell number n is given, the number of electrons is equal to 2×n2. So, if we're looking here at the first shell where n=1, that would mean that we have 2×12, which is 2×1, so the first shell can hold a maximum of 2 electrons. The second shell here, n=2, that'd be 2×22, which would be 2×4, which equals 8 electrons max that it can hold. So remember, if they only give you the n value, then you can use 2×n2 to determine the total number of electrons found within that given shell.

Electronic Structure: Number of Electrons Example 1

Here we have to determine how many electrons can be found in the 7th shell of an atom. So remember, the 7th shell corresponds to n equals 7. When we only know the shell number, the number of electrons is just equal to:

E = 2 ∙ n 2

So that will equal 2 ∙ 72. 7 squared is 49, and multiplying it by 2 means that we can have theoretically up to 98 electrons within the 7th shell of a given atom. So that would mean that option d would be our correct answer.

Theoretically, how many total electrons can be found in the 6th shell of an atom?

• A. 18
• B. 72
• C. 8
• D. 32

An element possesses 4 energy levels. How many total electrons can it theoretically hold?

• A. 72
• B. 100
• C. 110
• D. 60

Here’s what students ask on this topic:

How do you determine the maximum number of electrons in an electron shell?

The maximum number of electrons in an electron shell can be determined using the formula $2n^2$, where $n$ is the principal quantum number of the shell. For example, for the first shell ($n=1$), the maximum number of electrons is $21^2=2$. For the second shell ($n=2$), it is $22^2=8$. This formula helps in understanding the electron configuration and the structure of atoms.

What is the electron capacity of the second shell in an atom?

The electron capacity of the second shell in an atom can be calculated using the formula $2n^2$. For the second shell, $n=2$. Therefore, the maximum number of electrons it can hold is $22^2=8$. This means the second shell can accommodate up to 8 electrons.

Why is the formula 2(n)^2 used to determine the number of electrons in a shell?

The formula $2n^2$ is used to determine the number of electrons in a shell because it accounts for the quantum mechanical principles governing electron distribution. The principal quantum number $n$ indicates the shell level, and the formula considers both the number of orbitals in a shell and the Pauli exclusion principle, which states that each orbital can hold a maximum of two electrons. This formula helps in understanding the electron configuration and the structure of atoms.

How many electrons can the first shell of an atom hold?

The first shell of an atom, where the principal quantum number $n=1$, can hold a maximum of 2 electrons. This is determined using the formula $2n^2$. For $n=1$, the calculation is $21^2=2$. This means the first shell can accommodate up to 2 electrons.

What is the significance of the principal quantum number (n) in determining electron capacity?

The principal quantum number ($n$) is significant in determining electron capacity because it indicates the energy level or shell of an atom. The formula $2n^2$ uses $n$ to calculate the maximum number of electrons that can occupy a given shell. For example, for $n=1$, the first shell can hold 2 electrons, and for $n=2$, the second shell can hold 8 electrons. This helps in understanding the electron configuration and the structure of atoms.