/*! 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 1 Iron atoms have been detected in... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

Iron atoms have been detected in the sun's outer atmosphere, some with many of their electrons stripped away. What is the net electric charge (in coulombs) of an iron atom with 26 protons and 7 electrons? Be sure to include the algebraic sign ( \(+\) or \(-\) ) in your answer.

Short Answer

Expert verified
The net electric charge is \(+3.04 \times 10^{-18}\) coulombs.

Step by step solution

01

Understanding Protons and Electrons

An iron atom typically contains 26 protons. Each proton carries a positive charge of approximately \(1.6 \times 10^{-19}\) coulombs. This means the total positive charge due to the protons is \(26 \times 1.6 \times 10^{-19}\).
02

Calculating Total Positive Charge

Calculate the total positive charge from the protons: \(26 \times 1.6 \times 10^{-19} = 4.16 \times 10^{-18}\) coulombs.
03

Understanding Electrons in the Atom

This particular iron atom only has 7 electrons in its outer shell, each carrying a single negative charge of \(-1.6 \times 10^{-19}\) coulombs. Thus, the total negative charge of the electrons is \(7 \times (-1.6 \times 10^{-19})\).
04

Calculating Total Negative Charge

Calculate the total negative charge from the electrons: \(7 \times (-1.6 \times 10^{-19}) = -1.12 \times 10^{-18}\) coulombs.
05

Finding Net Electric Charge

The net electric charge of the atom is the sum of its positive and negative charges. So, the net charge is \(4.16 \times 10^{-18} + (-1.12 \times 10^{-18}) = 3.04 \times 10^{-18}\) coulombs.

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 91Ó°ÊÓ!

Key Concepts

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

Protons and Electrons
Understanding the basics of protons and electrons is essential when discussing electric charge. Protons are positively charged particles found in the nucleus of an atom. Their main role is contributing to the mass and charge of the atom. Each proton has an electric charge of approximately \(1.6 \times 10^{-19}\) coulombs.

Electrons, on the other hand, are negatively charged particles located in the electron cloud surrounding the nucleus. They have an equal but opposite charge to protons, which is \(-1.6 \times 10^{-19}\) coulombs. This means they can effectively neutralize the positive charge of protons if present in equal numbers.

For a neutral atom, the number of protons equals the number of electrons, balancing out the total charge. However, if electrons are added or removed, the atom becomes charged, forming what is known as an ion.
Ionization
Ionization is the process by which an atom or a molecule gains or loses electrons, resulting in a net electric charge. It transforms a neutral atom or molecule into an ion, which can be either positively or negatively charged.

  • Positive ion (cation): Formed when an atom loses electrons. It has more protons than electrons, resulting in a positive charge.
  • Negative ion (anion): Formed when an atom gains electrons, resulting in more electrons than protons, giving a negative charge.
This is particularly significant in contexts like the sun's outer atmosphere, where high energy conditions can strip electrons from atoms. This stripping leaves behind positively charged ions, as seen with iron ions which can lose many electrons due to the surrounding environment.

In the exercise, the iron atom becomes ionized by losing 19 of its 26 electrons, retaining only 7, which results in a net positive charge.
Coulomb's Law
Coulomb's Law is a fundamental principle describing the electrostatic interaction between charged particles. It explains how the force between two charged objects acts and how the magnitude of this force is determined.

According to Coulomb's Law, the force \( F \) between two point charges \( q_1 \) and \( q_2 \) is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance \( r \) between them:\[F = k \frac{|q_1 q_2|}{r^2} \]Here, \( k \) represents the electrostatic constant, approximately \(8.99 \times 10^9 \text{ N} \cdot \text{m}^2/\text{C}^2\).

The law is vital in calculating forces in simple electric systems and understanding interactions at an atomic level. It is essential when considering the attraction between electrons and protons or evaluating forces within ionized gas clouds, such as those found in stellar atmospheres, where charged particles constantly interact.

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

A spherical surface completely surrounds a collection of charges. Find the electric flux through the surface if the collection consists of (a) a single \(+3.5 \times 10^{-6} \mathrm{C}\) charge, (b) a single \(-2.3 \times 10^{-6} \mathrm{C}\) charge, and (c) both of the charges in (a) and (b).

The total electric field \(\overrightarrow{\mathbf{E}}\) consists of the vector sum of two parts. One part has a magnitude of \(E_{1}=1200 \mathrm{N} / \mathrm{C}\) and points at an angle \(\theta_{1}=35^{\circ}\) above the \(+x\) axis. The other part has a magnitude of \(E_{2}=1700\) \(\mathrm{N} / \mathrm{C}\) and points at an angle \(\theta_{2}=55^{\circ}\) above the \(+x\) axis. Find the magnitude and direction of the total field. Specify the directional angle relative to the \(+x\) axis.

A charge of \(-3.00 \mu \mathrm{C}\) is fixed at the center of a compass. Two additional charges are fixed on the circle of the compass, which has a radius of \(0.100 \mathrm{m} .\) The charges on the circle are \(-4.00 \mu \mathrm{C}\) at the position due north and \(+5.00 \mu \mathrm{C}\) at the position due east. What are the magnitude and direction of the net electrostatic force acting on the charge at the center? Specify the direction relative to due east.

An unstrained horizontal spring has a length of \(0.32 \mathrm{m}\) and a spring constant of \(220 \mathrm{N} / \mathrm{m}\). Two small charged objects are attached to this spring, one at each end. The charges on the objects have equal magnitudes. Because of these charges, the spring stretches by \(0.020 \mathrm{m}\) relative to its unstrained length. Determine (a) the possible algebraic signs and (b) the magnitude of the charges.

Two particles, with identical positive charges and a separation of \(2.60 \times 10^{-2} \mathrm{m},\) are released from rest. Immediately after the release, particle 1 has an acceleration \(\overrightarrow{\mathbf{a}}_{1}\) whose magnitude is \(4.60 \times 10^{3} \mathrm{m} / \mathrm{s}^{2},\) while particle 2 has an acceleration \(\overrightarrow{\mathbf{a}}_{2}\) whose magnitude is \(8.50 \times 10^{3} \mathrm{m} / \mathrm{s}^{2}\). Particle 1 has a mass of \(6.00 \times 10^{-6} \mathrm{kg} .\) Find \((\mathrm{a})\) the charge on each particle and \((\mathrm{b})\) the mass of particle 2.

See all solutions

Recommended explanations on Physics Textbooks

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.