Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 6: Problem 35

Does the hydrogen atom "expand" or "contract" when an electron is excited from the \(n=1\) state to the \(n=3\) state?

Short Answer

Expert verified
When an electron in a hydrogen atom is excited from the \(n=1\) state to the \(n=3\) state, the average distance of the electron from the nucleus increases, as calculated using the formula \(r_n = a_0n^2\). Since the average distance is greater in the \(n=3\) state compared to the \(n=1\) state, the hydrogen atom "expands" during this transition.

Step by step solution

01

Recall the Bohr Model for Hydrogen Atom

The Bohr model is a simplified model of a hydrogen atom where the electron orbits around the nucleus in specific energy levels. Each energy level is represented by an integer number called the principal quantum number, denoted by n.
02

Understand the meaning of "expanding" and "contracting"

As an electron moves from a lower energy level to a higher energy level, its average distance from the nucleus, also known as the radius of the orbital, tends to increase. If the average distance (radius) increases, then the hydrogen atom is said to "expand." Conversely, if the average distance (radius) decreases, the hydrogen atom is said to "contract."
03

Calculate the average distance of the electron in energy levels n=1 and n=3

The average distance of the electron in the nth orbital can be calculated using the formula: \(r_n = a_0n^2\), where \(a_0\) is the Bohr radius and roughly equals \(5.29 \times 10^{-11}\) meters. For n=1: \(r_1 = a_0(1)^2 = a_0\) For n=3: \(r_3 = a_0(3)^2 = 9a_0\) Now we need to compare these distances.
04

Compare the average distances to determine if the hydrogen atom expands or contracts

Since \(r_3 = 9a_0\) is larger than \(r_1 = a_0\), it means that the electron is on average farther from the nucleus when it is in the n=3 state than when it is in the n=1 state. Therefore, the hydrogen atom "expands" when an electron is excited from the n=1 state to the n=3 state.

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

The rays of the Sun that cause tanning and burning are in the ultraviolet portion of the electromagnetic spectrum. These rays are categorized by wavelength. So-called UV-A radiation has wavelengths in the range of $320-380 \mathrm{nm},\( whereas UV-B radiation has wavelengths in the range of \)290-320 \mathrm{nm}$. (a) Calculate the frequency of light that has a wavelength of \(380 \mathrm{nm} .\) (b) Calculate the energy of a mole of \(380-\mathrm{nm}\) photons. (c) Which are more energetic, photons of UV-A radiation or photons of UV-B radiation? (d) The UV-B radiation from the Sun is considered a more important cause of sunburn in humans than UV-A radiation. Is this observation consistent with your answer to part (c)?

If human height were quantized in 1 -cm increments, what would happen to the height of a child as she grows up: (i) the child's height would never change, (ii) the child's height would continuously increase, (iii) the child's height would increase in jumps of \(6 \mathrm{~cm}\), or (iv) the child's height would increase in "jumps" of \(1 \mathrm{~cm}\) at a time?

Consider a transition of the electron in the hydrogen atom from \(n=8\) to \(n=3\). (a) Is \(\Delta E\) for this process positive or negative? (b) Determine the wavelength of light that is associated with this transition. Will the light be absorbed or emitted? (c) In which portion of the electromagnetic spectrum is the light in part (b)?

State where in the periodic table these elements appear: (a) elements with the valence-shell electron configuration \(n s^{2} n p^{5}\) (b) elements that have three unpaired \(p\) electrons (c) an element whose valence electrons are \(4 s^{2} 4 p^{1}\) (d) the \(d\) -block elements [Section 6.9\(]\)

In the experiment shown schematically below, a beam of neutral atoms is passed through a magnetic field. Atoms that have unpaired electrons are deflected in different directions in the magnetic field depending on the value of the electron spin quantum number. In the experiment illustrated, we envision that a beam of hydrogen atoms splits into two beams. (a) What is the significance of the observation that the single beam splits into two beams? (b) What do you think would happen if the strength of the magnet were increased? (c) What do you think would happen if the beam of hydrogen atoms were replaced with a beam of helium atoms? Why? (d) The relevant experiment was first performed by Otto Stern and Walter Gerlach in \(1921 .\) They used a beam of \(\mathrm{Ag}\) atoms in the experiment. By considering the electron configuration of a silver atom, explain why the single beam splits into two beams.
See all solutions

Recommended explanations on Chemistry Textbooks

Nuclear Chemistry

Read Explanation

Ionic and Molecular Compounds

Read Explanation

Organic Chemistry

Read Explanation

Chemical Reactions

Read Explanation

Chemistry Branches

Read Explanation

Kinetics

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