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Chapter 7: Problem 68

Give the notation (using letter designations for \(l\) ) for the subshells denoted by the following quantum numbers. a. \(n=3, l=2\) b. \(n=4, l=0\) c. \(n=4, l=1\) d. \(n=5, l=3\)

Short Answer

Expert verified
a. 3d, b. 4s, c. 4p, d. 5f

Step by step solution

01

Understanding Quantum Numbers

The quantum number \( n \) is the principal quantum number and it indicates the energy level of the electron shell. The quantum number \( l \) is the azimuthal quantum number (also known as the angular momentum quantum number) and it defines the shape of the subshell. The values of \( l \) range from 0 up to \( n-1 \). Common notations for \( l \) include: \( l=0 \) is \( s \), \( l=1 \) is \( p \), \( l=2 \) is \( d \), \( l=3 \) is \( f \), \( l=4 \) is \( g \).
02

Connecting Quantum Numbers to Notation

To identify the subshell notation, combine the principal quantum number \( n \) with the letter corresponding to the azimuthal quantum number \( l \). For example, \( n=3, l=2 \) corresponds to the third energy level and \( d \) subshell, which is written as \( 3d \).
03

Solving for Part a

For \( n=3, l=2 \), the value of \( l \) corresponds to \( d \). Thus, the subshell is denoted as \( 3d \).
04

Solving for Part b

For \( n=4, l=0 \), the value of \( l \) corresponds to \( s \). Thus, the subshell is denoted as \( 4s \).
05

Solving for Part c

For \( n=4, l=1 \), the value of \( l \) corresponds to \( p \). Thus, the subshell is denoted as \( 4p \).
06

Solving for Part d

For \( n=5, l=3 \), the value of \( l \) corresponds to \( f \). Thus, the subshell is denoted as \( 5f \).

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Key Concepts

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

Principal Quantum Number
The principal quantum number, denoted by \( n \), is a fundamental concept in quantum mechanics that indicates the energy level of an electron in an atom. Think of \( n \) as defining the 'shell' in which an electron resides. This value can be any positive integer (1, 2, 3,...) and each value of \( n \) corresponds to a different energy level.
  • Higher values of \( n \) mean electrons are further from the nucleus and have higher energy.
  • The principal quantum number also determines the maximum number of electrons that can occupy a shell, calculated using the formula \( 2n^2 \).
  • For example, if \( n = 3 \), this shell can hold up to 18 electrons.
Understanding \( n \) helps us predict the general energy and location of electrons, crucial for comprehending an atom's structure and reactivity.
Azimuthal Quantum Number
The azimuthal quantum number, designated as \( l \), is also known as the angular momentum quantum number. This number describes the shape of the electron subshell, giving us insight into how electrons occupy space. The value of \( l \) depends on the principal quantum number, \( n \).
  • It ranges from 0 to \( n-1 \). For instance, if \( n=3 \), \( l \) can be 0, 1, or 2.
  • Each \( l \) value corresponds to a specific subshell shape: \( l=0 \) is an \( s \) subshell, \( l=1 \) is a \( p \) subshell, \( l=2 \) is \( d \), \( l=3 \) is \( f \), and so on.
Understanding \( l \) is essential for visualizing electron distribution within an atom and predicting chemical behavior.
Electron Subshells
Electron subshells describe the more detailed arrangement of electrons within an energy level. These subshells are determined by the azimuthal quantum number \( l \). Each subshell can hold a specific number of electrons, and this capacity plays a significant role in chemical bonding and electron configuration.
  • The \( s \) subshell holds up to 2 electrons.
  • The \( p \) subshell can accommodate 6 electrons.
  • The \( d \) subshell holds up to 10 electrons.
  • Finally, the \( f \) subshell can hold 14 electrons.
Electrons fill subshells in a manner that starts with the lowest energy state. This arrangement influences how substances interact on a fundamental level.
Subshell Notation
Subshell notation is a shorthand way to describe the position of electrons in an atom's electron configuration. It combines the principal quantum number \( n \) and the letter corresponding to the azimuthal quantum number \( l \). This notation succinctly expresses an electron's energy level and subshell type.
  • The notation is structured by first writing the number \( n \), followed by the letter for \( l \) (such as s, p, d, or f).
  • For example, \( n=3 \) and \( l=2 \) becomes "3d".
  • Similarly, \( n=4 \) and \( l=0 \) becomes "4s".
This system simplifies the representation of electron arrangements, aiding in visualizing electron configurations and understanding atomic interactions across different elements.

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Most popular questions from this chapter

What is the notation for the subshell in which \(n=4\) and \(l=3\) ? How many orbitals are in this subshell?

What is the wavelength of the transition from \(n=5\) to \(n=3\) for \(\mathrm{Li}^{2+} ?\) In what region of the spectrum does this emission occur? \(\mathrm{Li}^{2+}\) is a hydrogen-like ion. Such an ion has a nucleus of charge \(+Z e\) and a single electron outside this nucleus. The energy levels of the ion are \(-Z^{2} R_{\mathrm{H}} / n^{2}\), where \(Z\) is the atomic number.

How can gamma rays that are used in food irradiation be produced? Does such irradiated food show any radioactivity?

An atom in its ground state absorbs a photon (photon 1 ), then quickly emits another photon (photon 2). One of these photons corresponds to ultraviolet radiation, whereas the other one corresponds to red light. Explain what is happening. Which electromagnetic radiation, ultraviolet or red light, is associated with the emitted photon (photon 2)?

A particular microwave oven delivers 800 watts. (A watt is a unit of power, which is the joules of energy delivered, or used, per second.) If the oven uses microwave radiation of wavelength \(12.2 \mathrm{~cm}\), how many photons of this radiation are required to heat \(1.00 \mathrm{~g}\) of water \(1.00^{\circ} \mathrm{C}\), assuming that all of the photons are absorbed?
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