/*! 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 59 The number of orbitals in 3rd or... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 32: Problem 59

The number of orbitals in 3rd orbit are : (a) 3 . (b) 10 (c) 18 (d) none of these

Short Answer

Expert verified
The number of orbitals in the 3rd orbit is 9; answer is (d) none of these.

Step by step solution

01

Understand the Quantum Number n

The principal quantum number, denoted by \(n\), specifies the energy level or shell of an electron in an atom. For the 3rd energy level, \(n = 3\).
02

Determine Subshells in the 3rd Energy Level

The different subshells in any given energy level \(n\) are determined by the azimuthal quantum number \(l\), which can range from 0 up to \(n-1\). Therefore, the subshells for \(n = 3\) are \(l = 0\) (s), \(l = 1\) (p), and \(l = 2\) (d).
03

Find the Number of Orbitals in Each Subshell

The number of orbitals in a subshell is determined by the magnetic quantum number \(m_l\), which can range from \(-l\) to \(+l\). Consequently: - The s subshell (\(l = 0\)) has 1 orbital.- The p subshell (\(l = 1\)) has 3 orbitals.- The d subshell (\(l = 2\)) has 5 orbitals.
04

Add the Number of Orbitals

Add the number of orbitals in each subshell for \(n = 3\): \[1 \text{ (s) } + 3 \text{ (p) } + 5 \text{ (d) } = 9 \text{ orbitals in total.}\]
05

Compare with Options

None of the given options (3, 10, 18) suggest 9 orbitals. Thus, the correct answer is 'none of these'.

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.

Principal Quantum Number
The principal quantum number, denoted by \( n \), is a fundamental concept in quantum mechanics that defines the energy level or shell of an electron within an atom. It is an integer value that begins at 1 and can theoretically extend to infinity. The value of \( n \) is crucial because it determines the size of the electron cloud; the larger the number, the further the electron is from the nucleus and the more energy it has.
  • \( n = 1 \): Closest to the nucleus, also known as the ground state.
  • \( n = 2 \): Second energy level, electrons are further out than those in the first shell.
  • \( n = 3 \): Third energy level, this is the level in question for determining the number of orbitals available.
Understanding \( n \) is vital for determining other characteristics of the atom, as it directly affects the azimuthal and magnetic quantum numbers. In the context of the original exercise, \( n = 3 \) means we are looking at the third energy level.
Azimuthal Quantum Number
The azimuthal quantum number, represented by \( l \), provides information about the shape and the number of subshells within a given energy level. It ranges from 0 to \( n-1 \). Each value of \( l \) corresponds to a different type of subshell:
  • \( l = 0 \): s subshell
  • \( l = 1 \): p subshell
  • \( l = 2 \): d subshell

For example, at the third energy level (\( n = 3 \)) in the exercise, \( l \) can take on three values: 0, 1, and 2. Consequently, there are s, p, and d subshells available:
  • \( l = 0 \): Corresponds to a s subshell with 1 orbital.
  • \( l = 1 \): Corresponds to a p subshell with 3 orbitals.
  • \( l = 2 \): Corresponds to a d subshell with 5 orbitals.
Thus, knowing \( l \) helps in understanding the distribution and behavior of electrons across subshells within an energy level.
Magnetic Quantum Number
The magnetic quantum number, denoted by \( m_l \), describes the orientation of an orbital within a subshell. It also determines the number of orbitals within each subshell. The values of \( m_l \) range from \(-l\) to \(+l\), including zero.
  • If \( l = 0 \), then \( m_l = 0 \). This means one orbital for the s subshell.
  • If \( l = 1 \), then \( m_l = -1, 0, +1 \). This results in three orbitals for the p subshell.
  • If \( l = 2 \), then \( m_l = -2, -1, 0, +1, +2 \). This gives five orbitals for the d subshell.

The number of orbitals is crucial for understanding the possible electron configurations in an atom. For the 3rd energy level (\( n = 3 \)) discussed in the exercise, the calculation yields:
  • 1 orbital from s subshell
  • 3 orbitals from p subshell
  • 5 orbitals from d subshell

Summing these, the total number of orbitals is 9. This reinforces the understanding that quantum numbers are key for deciphering atomic structure and electron distribution.

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

In \(2 p^{\circ}\) electronic configuration only two electrons have the same spin quantum number. Which of the following statements is wrong about it? (a) This is against the Hund's rule (b) This is excited state (c) This can be represented by \(1 / 11\) (d) This is not possible

A photon of energy \(15 \mathrm{eV}\) collides with H-atom. Due to this collision, H-atom gets ionized. The maximum kinetic energy of emitted electron is : (a) \(1.4 \mathrm{eV}\) (b) \(5 \mathrm{eV}\) (c) \(15 \mathrm{eV}\) (d) \(13.6 \mathrm{eV}\)

Stability of half filled sub-shell is caused by : (a) exchange energy (b) greater spin multiplicity (c) both (a) and (b) (d) none of the above

Number of lobes of \(2 p\) -orbital as in \(y z\) - plane is : (a) 2 (b) 4 (c) 6 (d) 8

In Moseley's equation, \(\sqrt{V}=a(Z-b)\), which was derived from the observations made during the bombardment of metal target with X-rays : (a) \(a\) is independent but \(b\) depends on metal (b) both \(a\) and \(b\) are independent to the metal (c) both \(a\) and \(b\) depend on the metal (d) \(b\) is independent but \(a\) depends on the metal
See all solutions

Recommended explanations on Physics Textbooks

Electromagnetism

Read Explanation

Space Physics

Read Explanation

Nuclear Physics

Read Explanation

Force

Read Explanation

Wave Optics

Read Explanation

Engineering Physics

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.