Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 7: Problem 11

Which is larger, the H 1s orbital or the Li 1s orbital? Why? Which has the larger radius, the H atom or the Li atom? Why?

Short Answer

Expert verified
The Li 1s orbital is smaller than the H 1s orbital due to the higher effective nuclear charge experienced by the Li 1s electron (3) compared to the H 1s electron (1). However, the Li atom has a larger atomic radius than the H atom because it has more electron shells.

Step by step solution

01

Understand the concept of effective nuclear charge

Effective nuclear charge (Zeff) is the net charge experienced by an electron in an atom due to the attractive force of the protons and the repulsive force of the other electrons present. It is the difference between the total nuclear charge (Z) and the shielding constant (S). Mathematically, it can be represented as: \(Z_{eff} = Z - S\)
02

Find the effective nuclear charge for the H 1s and Li 1s orbitals

For hydrogen (H), there is only one electron and one proton in the atom. Therefore, there is no shielding effect. The effective nuclear charge experienced by the H 1s electron is equal to the total nuclear charge, which is 1. For lithium (Li), there are three electrons and three protons in the neutral atom. The two 1s electrons shield the outermost 2s electron from the full nuclear charge, but since we are considering the 1s orbital, shielding is negligible because the other 1s electron cannot shield the electron in focus. The effective nuclear charge experienced by the Li 1s electron is approximately equal to the total nuclear charge, which is 3.
03

Compare the size of H 1s and Li 1s orbitals

The size of an atomic orbital is inversely proportional to the effective nuclear charge experienced by the electron occupying that orbital. Since the Li 1s electron experiences a higher effective nuclear charge (3) compared to the H 1s electron (1), the Li 1s orbital is smaller than the H 1s orbital.
04

Find the atomic radii of H and Li atoms

Atomic radii increase down a group and decrease across a period in the periodic table. Hydrogen and lithium are both in Group 1 (alkali metals), but lithium is in Period 2, whereas hydrogen is in Period 1. Lithium has more electron shells, resulting in a larger atomic radius.
05

Summarize the results

In summary, the H 1s orbital is larger than the Li 1s orbital due to the difference in effective nuclear charge. However, the atomic radius of the Li atom is larger than the H atom because it has more electron shells. The bigger orbital size for H 1s does not necessarily mean that the overall size of the hydrogen atom is larger than the lithium atom.

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

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

Although no currently known elements contain electrons in g orbitals in the ground state, it is possible that these elements will be found or that electrons in excited states of known elements could be in \(g\) orbitals. For \(g\) orbitals, the value of \(\ell\) is \(4 .\) What is the lowest value of \(n\) for which \(g\) orbitals could exist? What are the possible values of \(m_{\ell} ?\) How many electrons could a set of \(g\) orbitals hold?

Without looking at data in the text, sketch a qualitative graph of the third ionization energy versus atomic number for the elements Na through Ar, and explain your graph.

In the ground state of cadmium, Cd, a. how many electrons have \(\ell=2\) as one of their quantum numbers? b. how many electrons have \(n=4\) as one of their quantum numbers? c. how many electrons have \(m_{\ell}=-1\) as one of their quantum numbers? d. how many electrons hav \(m_{s}=-\frac{1}{2}\) as one of their quantum numbers?

It takes \(7.21 \times 10^{-19} \mathrm{J}\) of energy to remove an electron from an iron atom. What is the maximum wavelength of light that can do this?

In defining the sizes of orbitals, why must we use an arbitrary value, such as 90% of the probability of finding an electron in that region?
See all solutions

Recommended explanations on Chemistry Textbooks

Kinetics

Read Explanation

The Earths Atmosphere

Read Explanation

Nuclear Chemistry

Read Explanation

Physical Chemistry

Read Explanation

Organic Chemistry

Read Explanation

Ionic and Molecular Compounds

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.

Sign-up for free