Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 2: Problem 39

From the information in this chapter on the mass of the proton, the mass of the electron, and the sizes of the nucleus and the atom, calculate the densities of a hydrogen nucleus and a hydrogen atom.

Short Answer

Expert verified
The densities of a hydrogen nucleus and a hydrogen atom can be calculated using the following information: - Proton mass (m_p): \(1.67 \times 10^{-27}\) kg - Electron mass (m_e): \(9.11 \times 10^{-31}\) kg - Nucleus size (r_p): \(1.2 \times 10^{-15}\) m - Atom size (r_a): \(5.3 \times 10^{-11}\) m By using the sphere volume formula and calculating the mass of the hydrogen atom (m_a = m_p + m_e), the densities are found as follows: - Hydrogen nucleus density (ρ_p) = \(m_p / V_p\) - Hydrogen atom density (ρ_a) = \(m_a / V_a\)

Step by step solution

01

1. Mass of proton, mass of electron, and sizes of the nucleus and atom

We will be using the following constants: Mass of proton (m_p): 1.67 x 10^{-27} kg Mass of electron (m_e): 9.11 x 10^{-31} kg Size of the nucleus (r_p): 1.2 x 10^{-15} m (approx.) Size of the hydrogen atom (r_a): 5.3 x 10^{-11} m (approx.)
02

2. Calculate the volume of the hydrogen nucleus and the hydrogen atom

We can calculate the volume of the hydrogen nucleus and hydrogen atom using the formula for the volume of a sphere: Volume of hydrogen nucleus (V_p) = (4/3) * π * r_p^3 Volume of hydrogen atom (V_a) = (4/3) * π * r_a^3
03

3. Calculate the mass of the hydrogen atom

The mass of the hydrogen atom (m_a) is the sum of the mass of the proton and the mass of the electron: m_a = m_p + m_e
04

4. Calculate the densities of hydrogen nucleus and hydrogen atom

Now, we can calculate the densities of the hydrogen nucleus and hydrogen atom using the formula density = mass/volume: Density of hydrogen nucleus (ρ_p) = m_p / V_p Density of hydrogen atom (ρ_a) = m_a / V_a

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

Write the atomic symbol \(\left({ }_{z}^{A} X\right)\) for each of the isotopes described below. a. number of protons \(=27\), number of neutrons \(=31\) b. the isotope of boron with mass number 10 c. \(Z=12, A=23\) d. atomic number 53, number of neutrons \(=79\) e. \(Z=9\), number of neutrons \(=10\) f. number of protons \(=29\), mass number 65

The two most reactive families of elements are the halogens and the alkali metals. How do they differ in their reactivities?

Four \(\mathrm{Fe}^{2+}\) ions are key components of hemoglobin, the protein that transports oxygen in the blood. Assuming that these ions are \({ }^{53} \mathrm{Fe}^{2+}\), how many protons and neutrons are present in each nucleus, and how many electrons are present in each ion?

Chlorine has two natural isotopes: \({ }_{1}^{\mathrm{j}} \mathrm{Cl}\) and \({ }_{1}{ }^{35} \mathrm{Cl} .\) Hydrogen reacts with chlorine to form the compound \(\mathrm{HCl}\). Would a given amount of hydrogen react with different masses of the two chlorine isotopes? Does this conflict with the law of definite proportion? Why or why not?

Carbon- 14 dating is a method used to determine the age of historical artifacts by examining the ratio of two isotopes of carbon (carbon- 14 and carbon-12). A living plant consumes carbon dioxide in the photosynthesis process and incorporates the carbon, including \({ }^{14} \mathrm{C}\), into its molecules. As long as a plant lives, the \({ }^{14} \mathrm{C} /{ }^{12} \mathrm{C}\) ratio in its molecules remains the same as in the atmosphere because of its continuous uptake of carbon. However, as soon as a tree is cut to make a wooden bowl or a flax plant is harvested to make linen, the \({ }^{14} \mathrm{C}^{12} \mathrm{C}\) ratio begins to decrease because of the radioactive decay of \({ }^{14} \mathrm{C}\left({ }^{12} \mathrm{C}\right.\) is stable). By comparing the current \({ }^{14} \mathrm{C} /{ }^{12} \mathrm{C}\) ratio to the presumed ratio when the artifact was made, one can estimate the age of the artifact. For carbon-14 and carbon- 12 , how many protons and neutrons are in each nucleus? Assuming neutral atoms, how many electrons are present in an atom of carbon- 14 and in an atom of carbon-12?
See all solutions

Recommended explanations on Chemistry Textbooks

Chemical Analysis

Read Explanation

Kinetics

Read Explanation

Ionic and Molecular Compounds

Read Explanation

Inorganic Chemistry

Read Explanation

The Earths Atmosphere

Read Explanation

Organic 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.

Sign-up for free