Quantum Numbers: Principal Quantum Number: Videos & Practice Problems

The principal quantum number ($n$) is fundamental in understanding atomic structure, as it defines the size and energy level of an atomic orbital. As $n$ increases, so does the size and energy of the orbital. This quantum number is directly tied to the periods or rows of the periodic table, with each shell corresponding to a specific period. Currently, there are seven periods, reflecting our current technological capabilities in discovering or synthesizing new elements. However, this is not a fixed number; as technology advances, we could potentially discover or create elements that would expand the periodic table beyond seven periods. The principal quantum number must be an integer starting from one and, theoretically, can extend to infinity, indicating that there could be an infinite number of periods in the future. Understanding $n$'s role is crucial for comprehending how electrons are arranged in atoms and their subsequent chemical behavior.

Principal Quantum Number

The principal quantum number, denoted as n, is a fundamental concept in quantum mechanics that describes the size and energy level of atomic orbitals. As the value of n increases, both the size of the shell and the energy level associated with that shell also increase. This relationship is crucial for understanding the structure of atoms and their arrangement in the periodic table.

Each principal quantum number corresponds to a specific shell, with n values ranging from 1 to 7 currently observed in the periodic table. For instance, n = 1 corresponds to the first shell, which is linked to period 1 of the periodic table, while n = 7 corresponds to the seventh shell, associated with period 7. This connection illustrates how the energy levels of electrons in an atom are organized according to the rows of the periodic table.

It is important to note that the periodic table is not a static entity; it evolves as new elements are discovered or synthesized. Currently, there are seven periods, but advancements in technology and exploration may lead to the identification of new elements, potentially expanding the periodic table to include more than seven rows in the future. Thus, the principal quantum number n can theoretically take on any positive integer value, starting from 1 and extending to infinity. This means that values such as n = 22 are conceivable, even if they have not yet been realized.

In summary, the principal quantum number is integral to understanding the size and energy of atomic orbitals, influencing the arrangement of elements in the periodic table and highlighting the dynamic nature of scientific discovery.

Principal Quantum Number Example

In quantum mechanics, the principal quantum number, denoted as \( n \), is a fundamental descriptor of an electron's energy level within an atom. This number indicates the shell in which an electron resides and is always a positive integer. The possible values for \( n \) start from 1 and extend theoretically to infinity, corresponding to the various energy levels or periods in the periodic table.When evaluating potential values for \( n \), it is essential to remember that negative integers and zero are not valid. Therefore, values such as \( n = -3 \), \( n = -4 \), \( n = 0 \), and \( n = -7 \) are excluded from consideration. The only acceptable values are positive integers, such as \( n = 1, 2, 3, \ldots \), and so forth. In this context, the value \( n = 11 \) is a valid principal quantum number, indicating a higher energy level that could theoretically exist in future elements beyond the current periodic table. Thus, the correct answer to the question regarding possible values for a principal quantum number shell is \( n = 11 \).

What is the value of n for the electron based on the image of the atom provided?

• A. n = 3
• B. n = 5
• C. n = 1
• D. n = 2
• E. n = 6

Answer: (D)

Which electron possesses the lowest possible energy from the image provided?

• A. A
• B. B
• C. C
• D. D
• E. E

Answer: (D)

Here’s what students ask on this topic:

What is the principal quantum number?

The principal quantum number, denoted as n, is a quantum number that specifies the energy level of an electron in an atom. It is one of four quantum numbers which describe the unique quantum state of an electron. The principal quantum number can take any positive integer value ($n=1,2,3,\dots$), and as it increases, it indicates an electron is in a higher energy level, or shell, further away from the nucleus.

The energy associated with each level increases as n increases. This means that electrons in higher principal quantum numbers are less tightly bound to the nucleus and have higher potential energy. In addition, the principal quantum number also determines the number of subshells available within a given shell, and thus, the maximum number of electrons that can occupy that shell. For example, for $n=2$, there are two subshells (2s and 2p), which can hold a total of 8 electrons. The principal quantum number is fundamental in understanding the electronic structure of atoms and the arrangement of electrons in various atomic orbitals.

What does the principal quantum number determine?

The principal quantum number, denoted as n, is a quantum number that fundamentally determines the energy level of an electron in an atom. It is an integer that can take on any positive value ($n=1,2,3,\dots$). The larger the value of n, the higher the energy level and the larger the orbit or shell in which the electron resides. As n increases, the electron can be found further from the nucleus, which means that the electron has a higher potential energy and is less tightly bound to the nucleus. This quantum number also indirectly influences other properties of the electron such as its orbital size and the number of possible subshells within a given energy level. For example, for $n=2$, there can be s and p subshells, leading to different shapes and orientations of the electron orbitals.

How can I find the principal quantum number?

The principal quantum number, often symbolized as n, is one of the four quantum numbers which describe the unique quantum state of an electron in an atom. It essentially defines the electron's shell or energy level. To find the principal quantum number, you need to look at the electron configuration of the atom or ion in question.

For instance, if you're considering a neutral atom of carbon, its electron configuration is 1s² 2s² 2p². The highest value of n in this configuration is 2, which means the outermost electrons of carbon are in the second energy level.

The principal quantum number n can take any positive integer value starting from 1 upwards. The larger the value of n, the higher the energy level and the farther the electron is from the nucleus, on average. Each energy level can hold up to 2n² electrons. So, you can determine n by looking at the period (row) of the element in the periodic table or by counting the energy levels in the electron configuration.