Question

Calculate the maximum number of electrons in \(1 \mathrm{st}\), 2nd, \(3 \mathrm{rd}\) and 4 th shells.

Short answer

Answer: The maximum number of electrons that can be accommodated in the 1st, 2nd, 3rd, and 4th shells of an atom are 2, 8, 18, and 32 electrons, respectively.

Step-by-step solution

Understanding the Shell Capacity Formula

We will use the formula \(2n^2\) to determine the maximum number of electrons that can be placed in a shell, where n represents the shell number. For example, if n=1 (1st shell), we can find the maximum number of electrons in that shell by calculating \(2(1)^2\). We will perform this calculation for all four shells.

Calculate Maximum Electrons in the 1st Shell

Using the shell capacity formula, we will now calculate the maximum number of electrons in the 1st shell (n=1). We have: \(2(1)^2 = 2(1) = 2\). Therefore, the maximum number of electrons that can be accommodated in the 1st shell is 2.

Calculate Maximum Electrons in the 2nd Shell

Next, we will calculate the maximum number of electrons in the 2nd shell (n=2) using the formula: \(2(2)^2 = 2(4) = 8\). So, the maximum number of electrons that can be accommodated in the 2nd shell is 8.

Calculate Maximum Electrons in the 3rd Shell

Now, we will calculate the maximum number of electrons in the 3rd shell (n=3) using the formula: \(2(3)^2 = 2(9) = 18\). Thus, the maximum number of electrons that can be accommodated in the 3rd shell is 18.

Calculate Maximum Electrons in the 4th Shell

Lastly, we will calculate the maximum number of electrons in the 4th shell (n=4) using the formula: \(2(4)^2 = 2(16) = 32\). Therefore, the maximum number of electrons that can be accommodated in the 4th shell is 32. The maximum number of electrons in each shell is: - 1st shell: 2 electrons - 2nd shell: 8 electrons - 3rd shell: 18 electrons - 4th shell: 32 electrons