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Which of the following represent impossible combinations of \(n\) and \(l:(\) a \() 1 p,(\) b \() 4 s,(c) 5 f,(\) d) \(2 d ?\)

Short Answer

Expert verified
The impossible combinations of \(n\) and \(l\) are 1p and 2d.

Step by step solution

01

Checking option (a) 1p

In this combination, n=1 and l is represented by the letter p, which corresponds to the value l=1. Since l must be between 0 and (n-1), l can only be 0 when n=1. Hence, the combination 1p is impossible.
02

Checking option (b) 4s

In this combination, n=4 and l is represented by the letter s, which corresponds to the value l=0. Since l must be between 0 and (n-1), and l=0 falls within this range when n=4, the combination 4s is possible.
03

Checking option (c) 5f

In this combination, n=5 and l is represented by the letter f, which corresponds to the value l=3. Since l must be between 0 and (n-1), and l=3 falls within this range when n=5, the combination 5f is possible.
04

Checking option (d) 2d

In this combination, n=2 and l is represented by the letter d, which corresponds to the value l=2. Since l must be between 0 and (n-1), l can only be 0 or 1 when n=2. Hence, the combination 2d is impossible. The impossible combinations of n and l are 1p and 2d.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Principle Quantum Number
The principle quantum number, denoted by the symbol \( n \), plays a fundamental role in determining the properties of electrons in an atom. It can take any positive integer value starting from 1, such as 1, 2, 3, and so on. Each of these numbers corresponds to a specific energy level or shell around the nucleus of an atom. The principle quantum number indicates:
  • The average distance of the electron cloud from the nucleus.
  • The overall size of the electron orbitals.
  • The energy level the electron resides in.
When \( n = 1 \), the electron is in the closest shell to the nucleus, and it has the lowest energy. As \( n \) increases, the electron's distance from the nucleus and energy increase as well.
This quantum number is crucial because it helps establish the basis for further quantum numbers, and provides a framework for understanding electron configurations.
Azimuthal Quantum Number
The azimuthal quantum number, denoted by \( l \), defines the shape of the electron orbital and is connected with the angular momentum of an electron in an atom. This value can range from 0 to \( n-1 \), meaning it depends on the principal quantum number \( n \). For instance, if \( n = 3 \), then \( l \) can have values of 0, 1, or 2. Each value of \( l \) corresponds to a particular type of orbital:
  • \( l = 0 \) signifies an s orbital.
  • \( l = 1 \) signifies a p orbital.
  • \( l = 2 \) signifies a d orbital.
  • \( l = 3 \) signifies an f orbital.
Considering the example exercise, option (a) \(1p\) is impossible because \( n = 1 \) means \( l \) can only be 0, making a "p" orbital not possible with \( n = 1 \). Option (d) \(2d\) is also impossible because \( n = 2 \) allows \( l \) values of only 0 or 1. Thus a "d" orbital, which needs \( l = 2 \), cannot exist in this scenario.
Electron Orbital Notation
Electron orbital notation is a way of describing the arrangement of electrons in an atom's electron shells and orbitals. Each orbital is described by a combination of \( n \), \( l \), and other quantum numbers. This notation is vital for:
  • Predicting the chemical properties of elements.
  • Understanding how atoms bond.
  • Visualizing the electron cloud around the nucleus.
In the exercise, we see examples of such notations like "4s," where each letter refers to the orbital shape given by the azimuthal quantum number \( l \) and comes after the principal quantum number \( n \) corresponding to the energy level. Correct electron orbital notation must follow the rules of quantum numbers, meaning the values of \( n \) and \( l \) must be consistent with their definitions. Therefore, notations like "1p" or "2d" in the exercise are impossible due to the restrictions on \( n \) and \( l \). Understanding these notations is essential for grasping the electron distribution in an atom effectively.

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