How Many Electrons Can Fit in a Shell with Principal Quantum Number n=4-

How many electrons can occupy the shell having n=4?

In the field of chemistry and quantum mechanics, understanding the electron configuration of atoms is crucial for explaining various chemical properties and behaviors. One key concept in this field is the maximum number of electrons that can occupy a particular shell of an atom. Specifically, let’s delve into the question: how many electrons can occupy the shell having n=4?

The electron configuration of an atom is determined by its atomic number, which is the number of protons in its nucleus. The shell, or principal energy level, is defined by the principal quantum number (n). In this case, we are examining the fourth shell, where n=4. The maximum number of electrons that can occupy a given shell is determined by the formula 2n^2, where n is the principal quantum number.

Applying this formula to the fourth shell, we get 2 4^2 = 2 16 = 32. Therefore, the fourth shell can accommodate a maximum of 32 electrons. However, it’s important to note that not all of these electrons will necessarily be present in an atom with an atomic number less than 32.

To understand this further, let’s take a look at the electron configuration of some elements in the fourth shell. For example, the noble gas krypton (Kr) has an atomic number of 36 and its electron configuration is 1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^10 4p^6. In this case, the fourth shell is fully occupied with 18 electrons (4s^2 3d^10 4p^6). On the other hand, the element zinc (Zn) has an atomic number of 30 and its electron configuration is 1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^10. Here, the fourth shell is still full, with 18 electrons.

In conclusion, the shell with n=4 can accommodate a maximum of 32 electrons. However, the actual number of electrons in an atom with an atomic number less than 32 will depend on the specific element’s electron configuration. Understanding this concept is essential for comprehending the behavior of atoms and their chemical properties.