/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 50 What is the maximum number of s ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 50

What is the maximum number of s orbitals found in a given electron shell? The maximum number of \(p\) orbitals? Of \(d\) orbitals? Of \(f\) orbitals?

Short Answer

Expert verified
1 s, 3 p, 5 d, and 7 f orbitals.

Step by step solution

01

Understanding Electron Shells and Orbitals

Each electron shell, characterized by the principal quantum number \( n \), can contain different types and numbers of orbitals. The types of orbitals each shell can have include s, p, d, and f, and as \( n \) increases, more types of orbitals become available.
02

Determining Maximum Number of s Orbitals

All electron shells, regardless of their level (\( n \)), contain exactly one s orbital. Therefore, the maximum number of s orbitals in any electron shell is 1.
03

Determining Maximum Number of p Orbitals

Starting from the second electron shell (\( n = 2 \)), each shell can have up to three p orbitals (p_x, p_y, and p_z). Thus, the maximum number of p orbitals in any electron shell is 3.
04

Determining Maximum Number of d Orbitals

From the third electron shell (\( n = 3 \)), each shell can have up to five d orbitals. Hence, the maximum number of d orbitals in any electron shell is 5.
05

Determining Maximum Number of f Orbitals

Beginning with the fourth electron shell (\( n = 4 \)), each shell can contain up to seven f orbitals. So, the maximum number of f orbitals in any electron shell is 7.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

s orbitals
The simplest type of electron orbital is the s orbital. Every electron shell, regardless of its principal quantum number \( n \), contains exactly one s orbital. This is because s orbitals have a shape that is perfectly spherical. They do not have preferred directions in space. Consequently, there is only one way to fit an s orbital within an electron shell. This uniformity makes them unique compared to other orbitals.
  • Every shell from \( n = 1 \) upwards has just one s orbital.
  • The s orbital can hold a maximum of two electrons because each orbital can accommodate two electrons with opposite spins.
The presence of one s orbital in every shell is a fundamental aspect of atomic structure. It's also the reason why the lowest energy sublevel in any electron shell is always the s sublevel.
p orbitals
P orbitals are introduced from the second electron shell, which means they start from \( n = 2 \). They are more complex than s orbitals, having a dumbbell-like shape, and are oriented in three different spatial directions: along the x, y, and z axes. This orientation leads to the presence of three different p orbitals in any given shell.
  • These orbitals are known as \( p_x \), \( p_y \), and \( p_z \).
  • Each p orbital can also hold up to two electrons, leading to a total capacity of six electrons for the p orbitals in one shell.
This structure allows for more flexibility and variation in electron distribution compared to the singular s orbital. The orientation and number of p orbitals play crucial roles in determining the geometry and bonding characteristics of molecules.
d orbitals
D orbitals become available starting at the third electron shell (\( n = 3 \)). They are more varied and complex in shape compared to s and p orbitals. D orbitals have clover-shaped structures, and there are five distinct d orbitals in any given shell.
  • The five d orbitals are often labeled as \( d_{xy} \), \( d_{xz} \), \( d_{yz} \), \( d_{x^2-y^2} \), and \( d_{z^2} \).
  • Each d orbital can accommodate two electrons, contributing to a total capacity of ten electrons across the d orbitals in a single shell.
The unique shapes and orientations of d orbitals are key to the chemistry of transition metals, which utilize these orbitals for bonding and electron exchange.
f orbitals
F orbitals are encountered beginning with the fourth electron shell, or \( n = 4 \). With even more complex shapes, f orbitals are essential for understanding the behavior of elements in the f-block, such as the lanthanides and actinides. A full set of f orbitals constitutes seven orbitals in total.
  • Each f orbital can hold up to two electrons, resulting in a total of fourteen electrons for all seven f orbitals in a given shell.
  • The complex shapes of f orbitals allow for unique bonding and chemical properties, especially significant in the field of rare earth chemistry.
While the f orbitals are not involved in the chemistry of most everyday elements, they are crucial for understanding complex electronic configurations and properties of heavy elements.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

The most prominent line in the emission spectrum of magnesium is \(285.2 \mathrm{nm} .\) Other lines are found at 383.8 and \(518.4 \mathrm{nm} .\) In what region of the electromagnetic spectrum are these lines found? Which is the most energetic line? What is the energy of 1.00 mol of photons with the wavelength of the most energetic line?

What does "wave-particle duality" mean? What are its implications in our modern view of atomic structure?

What is the maximum number of orbitals that can be identified by each of the following sets of quantum numbers? When "none" is the correct answer, explain your reasoning. (a) \(n=4, \ell=3\) (b) \(n=5\) (c) \(n=2, \ell=2\) (d) \(n=3, \ell=1, m_{\ell}=-1\)

Violet light has a wavelength of about \(410 \mathrm{nm}\). What is its frequency? Calculate the energy of one photon of violet light. What is the energy of 1.0 mol of violet photons? Compare the energy of photons of violet light with those of red light. Which is more energetic?

If energy is absorbed by a hydrogen atom in its ground state, the atom is excited to a higher energy state. For example, the excitation of an electron from \(n=1\) to \(n=3\) requires radiation with a wavelength of \(102.6 \mathrm{nm}\) Which of the following transitions would require radiation of longer wavelength than this? (a) \(n=2\) to \(n=4\) (b) \(n=1\) to \(n=4\) (c) \(n=1\) to \(n=5\) (d) \(n=3\) to \(n=5\)
See all solutions

Recommended explanations on Chemistry Textbooks

The Earths Atmosphere

Read Explanation

Ionic and Molecular Compounds

Read Explanation

Physical Chemistry

Read Explanation

Kinetics

Read Explanation

Chemical Analysis

Read Explanation

Inorganic Chemistry

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.