Problem 61 - Chemistry: The Central Science in SI Units, Global Edition

Question

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

Step-by-Step Solution

Answer

The impossible combinations of \(n\) and \(l\) are \(1p\) and \(2d\), as their respective \(l\) values are not within the possible range of \(0\) to \(n-1\).

Step 1: Option a: 1p

The given combination is \(1p\). Here, \(n=1\) and \(l=1\). Since \(l\) is equal to \(n\), it is not within the possible range of \(0\) to \(n-1\), which means the combination is impossible.

Step 2: Option b: 4s

The given combination is \(4s\). Here, \(n=4\) and \(l=0\). Since the possible range of \(l\) is \(0\) to \(n-1\) or in this case, \(0\) to \(3\), and \(l=0\), the 4s combination is possible.

Step 3: Option c: 5f

The given combination is \(5f\). Here, \(n=5\) and \(l=3\) (as we know, \(f=3\)). The possible range for \(l\) is \(0\) to \(n-1\) or in this case, \(0\) to \(4\). Since \(l=3\), the 5f combination is possible.

Step 4: Option d: 2d

The given combination is \(2d\). Here, \(n=2\) and \(l=2\) (as we know, \(d=2\)). The possible range for \(l\) is \(0\) to \(n-1\) or in this case, \(0\) to \(1\). Since \(l\) is equal to \(n\), it is not within the possible range, which means that the combination is impossible. So, the impossible combinations are \(1p\) and \(2d\).

Key Concepts

n (principal quantum number)

The principal quantum number, symbolized as \( n \), is one of the essential quantum numbers used to describe an electron's position in an atom. It tells us about the principal electron shell or energy level an electron occupies. The values of \( n \) are positive integers: \( 1, 2, 3, \ldots \). Each increase in \( n \) signifies a higher energy level and a larger atomic orbit. This concept is crucial because:

• \( n \) determines the overall size of the electron cloud.
• Higher \( n \) values indicate electrons that are farther from the nucleus, potentially having higher energy.
• The number of orbitals in a shell is given by \( n^2 \), and the maximum number of electrons a shell can hold is given by \( 2n^2 \).

To put it simply, \( n \) is like the address number in a huge apartment complex, providing information on which floor (energy level) to find the electron.

l (azimuthal quantum number)

The azimuthal quantum number, denoted as \( l \), reveals the subshell or shape of the electron's orbit. It is crucial in understanding finer details about electron distribution. For any given \( n \), \( l \) can have integer values ranging from \( 0 \) to \( n-1 \). This means:

• \( l \) defines the shape of the orbital (s, p, d, f). For instance, \( l=0 \) corresponds to an s orbital, \( l=1 \) to a p orbital, and so on.
• Possible \( l \) values inform us about the type of subshell present, influencing chemical properties and reactions.
• The combination of \( n \) and \( l \) must adhere to the rule where \( l \) cannot equal or exceed the value of \( n \).

Think of \( l \) as defining the type of room the electron stays in, like how different rooms have different layouts and purposes.

electron configuration

Electron configuration describes how electrons are distributed among available atomic orbitals. It follows a specific order based on increasing energy levels, known as the Aufbau principle. Understanding electron configuration is vital because it helps:

• Predict chemical properties and reactivity of elements.
• Understand how atoms bond in compounds.
• Identify and explain trends in the periodic table.

The electron configuration notation references the sublevel filling procedures (e.g., 1s, 2s, 2p), utilizing quantum numbers to allocate electrons precisely. For example, hydrogen has a simple configuration of 1s¹, while elements with more electrons need configurations that spread electrons across different subshells, respecting the Pauli exclusion principle and Hund's rule. Imagine electron configuration as mapping out the seating arrangement in a grand theater, ensuring that all seats (orbitals) are filled in a predefined order, following specific rules.