Electronic Structure: Number of Electrons: Videos & Practice Problems

An atom has electron shells, each with a maximum capacity for electrons determined by the formula $2^{\left(n\right)^2}$. For example, the first shell (n=1) can hold 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, when only the shell number n is given, the number of electrons is equal to 2×n2. If we're looking here at the first shell where n equals 1, that would mean that we have 2×12, which is 2 times 1, so the first shell can hold a maximum of 2 electrons. The second shell here, n equals 2, that'd be 2×n2, which would be 2 times 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=7. When we only know the shell number, the number of electrons is just equal to 2×n2. So that will equal 2×72. 72 is 49, and multiplying it by 2 means that we can have theoretically up to 98 electrons within the seventh 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

Answer: (B)

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

• A. 72
• B. 100
• C. 110
• D. 60

Answer: (D)

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 third shell in an atom?

The electron capacity of the third shell in an atom can be calculated using the formula $2n^2$, where $n$ is the principal quantum number. For the third shell, $n$ = 3. Therefore, the maximum number of electrons it can hold is $23^2=18$. This means the third shell can accommodate up to 18 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 incorporates the number of possible subshells and orbitals within that shell. Each orbital can hold a maximum of 2 electrons, and the formula ensures that all possible orbitals are considered, providing an accurate count of the maximum electron capacity for each shell.

How many electrons can the fourth shell hold?

The fourth shell in an atom can hold a maximum number of electrons determined by the formula $2n^2$, where $n$ is the principal quantum number. For the fourth shell, $n$ = 4. Therefore, the maximum number of electrons it can hold is $24^2=32$. This means the fourth shell can accommodate up to 32 electrons.

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

The principal quantum number ($n$) is significant in electron configuration as it indicates the main energy level or shell of an electron within an atom. It determines the size and energy of the shell, with higher $n$ values corresponding to shells that are further from the nucleus and have higher energy. The principal quantum number also helps in calculating the maximum number of electrons a shell can hold using the formula $2n^2$. Understanding $n$ is crucial for grasping the arrangement of electrons in atoms and their chemical properties.