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Chapter 3: Problem 85

Identify the symbols used to describe orbitals for which \(l=0,1,2,\) and \(3 .\)

Short Answer

Expert verified
The symbols are: \( l=0 \) is \( s \), \( l=1 \) is \( p \), \( l=2 \) is \( d \), and \( l=3 \) is \( f \).

Step by step solution

01

Understanding the Quantum Number l

The quantum number \( l \) is the azimuthal quantum number or angular momentum quantum number, which determines the shape of the orbital. Each value of \( l \) corresponds to a specific type of orbital symbol.
02

Defining the Orbital Symbols

Orbital symbols have specific letters that correspond to each value of \( l \): - When \( l = 0 \), the symbol is \( s \) (spherical shape).- When \( l = 1 \), the symbol is \( p \) (dumbbell shape).- When \( l = 2 \), the symbol is \( d \) (cloverleaf shape).- When \( l = 3 \), the symbol is \( f \) (complex shape).

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Key Concepts

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

Azimuthal Quantum Number
The azimuthal quantum number, denoted by the symbol \( l \), is an essential component in quantum mechanics. It's also known as the angular momentum quantum number. This quantum number provides key insights into the shape of an electron's orbital in an atom.
Azimuthal quantum numbers are whole numbers that range from 0 up to \( n-1 \), where \( n \) is the principal quantum number. This means that each value of \( l \) is associated with a specific orbital shape:
  • \( l = 0 \): Corresponds to the "s" orbital.
  • \( l = 1 \): Corresponds to the "p" orbital.
  • \( l = 2 \): Corresponds to the "d" orbital.
  • \( l = 3 \): Corresponds to the "f" orbital.
Understanding these values helps in predicting the electron cloud's shape around the nucleus, providing a deeper insight into chemical bonding and molecular structure.
Orbital Shapes
Orbital shapes are dictated by the value of the azimuthal quantum number \( l \), which directly determines the geometry of the regions in space where electrons are likely to be found.
Each different \( l \) value has a distinctive shape:
  • s Orbitals (\( l = 0 \)): These have a simple spherical shape. Regardless of the energy level, all s orbitals are symmetrical around the nucleus. This means that an s orbital's probability cloud is like a round balloon centered on the atom's core.
  • p Orbitals (\( l = 1 \)): These have a characteristic dumbbell shape. Each p orbital is oriented along a different axis (x, y, or z), forming three p orbitals in each energy level above the first.
  • d Orbitals (\( l = 2 \)): These exhibit more complex shapes, typically resembling a cloverleaf. These orbitals are crucial in transition metals, where they influence properties such as catalytic activity and coloration.
  • f Orbitals (\( l = 3 \)): These have very complex shapes that are not easily visualized. The intricate structures contribute to the distinctiveness of the lanthanides and actinides series in the periodic table.
Knowing these shapes is fundamental to understanding how electrons populate space around a nucleus, playing a pivotal role in chemistry and physics.
Orbital Symbols
Orbital symbols are used as a notation to represent the energy levels and shapes of atomic orbitals. These symbols simplify discussions and calculations in quantum mechanics.
Each value of the azimuthal quantum number \( l \) has a corresponding symbol:
  • s (\( l = 0 \)): Represents orbitals with spherical shapes.
  • p (\( l = 1 \)): Denotes the dumbbell-shaped orbitals.
  • d (\( l = 2 \)): Signifies the more complex, cloverleaf-shaped orbitals.
  • f (\( l = 3 \)): Refers to the most complex and varied orbital shapes.
These symbols allow for clear and efficient communication about an element's electronic configuration. When scientists talk about the electron arrangement in atoms, these symbols appear frequently in notations, making it easier to identify and predict element behaviors in chemical reactions.

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Most popular questions from this chapter

Atoms that have unpaired electrons are magnetic. Those that have no unpaired electrons are not magnetic. Which of the following atoms or ions are magnetic? Show your work. (a) \(\mathrm{H}\) (b) He (c) \(\mathrm{F}^{-}\) (d) \(\mathrm{Na}\) (e) \(\mathrm{Mg}\) (f) \(\mathrm{Si}\) (g) \(\mathrm{Cr}^{3+}\)

List the following elements in order of increasing second ionization energy. (a) Li (b) \(\mathrm{Be}\) (c) \(\mathrm{Na}\) (d) \(\mathrm{Mg}\) (e) \(\mathrm{Ne}\)

Why are valence electrons easier to remove from an atom than core electrons?

Which of the following neutral atoms has the largest number of unpaired electrons? (a) \(\mathrm{Na}\) (b) \(\mathrm{Al}\) (c) \(\mathrm{Si}\) (d) \(\mathrm{P}\) (e) \(\underline{S}\)

Which of the following contains sets of atoms or ions that have equivalent electron configurations? (a) \(\mathrm{B}^{3+}, \mathrm{C}^{4+}, \mathrm{H}^{+}, \mathrm{He}\) (b) \(\mathrm{Na}^{+}, \mathrm{Ne}, \mathrm{N}^{3+}, \mathrm{O}^{2-}\) (c) \(\mathrm{Mg}^{2+}, \mathrm{F}^{-}, \mathrm{Na}^{+}, \mathrm{O}^{2-}\) (d) \(\mathrm{Ne}, \mathrm{Ar}, \mathrm{Xe}, \mathrm{Kr}\) (e) \(\mathrm{O}^{2-}, \mathrm{S}^{2-}, \mathrm{Se}^{2-}, \mathrm{Te}^{2-}\)
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