Concept explainers
(a) Describe Rutherford’s experiment and how the results revealed the nuclear structure of the atom. (b) Consider the
Interpretation:
The Rutherford’s experiment and its result as nuclear structure of atom is to be described and the density of the nucleus in
Concept Introduction:
The Rutherford model of an atom is also known as the planetary model of the atom. It is used to describe the structure of the atom.
The density of a substance is defined as the measurement of mass per unit volume and is calculated as
Answer to Problem 120AP
Solution:
(a)
In the Rutherford model, the alpha particles are bombarded on gold foil, where some particles will pass and some will deflect back. The main observation is that the nucleus is present in the center of the atom and the size of the atom is larger than the size of the nucleus.
(b) The density of nucleus is
The density of the electron is
Explanation of Solution
a) The Rutherford’s experiment and the results that revealed the nuclear structure of the atom.
The Rutherford model carries out an experiment that when alpha particles are bombarded on thin gold foil, then most of the alpha particles pass through it and some are deflected back through it. The main observation of Rutherford is that a positive charge situated at the center is the nucleus and the size of the nucleus is smaller than the size of the atom. The average of scattering tells about the number of protons, which is based on their electrostatic interactions.
Given information: The radius of the nucleus is
and the radius of sodium is
b) The density of nucleus in
and density of the space occupied by the electrons outside the nucleus in the sodium atom. The results come out support Rutherford’s model of an atom.
As the nucleus have a spherical shape, so the volume of a sphere is to be calculated as follows:
Here,
Substitute the values in the above equation as:
Therefore, the volume of the nucleus is
The density of the nucleus is to be calculated as follows:
Substitute the value of the mass of the nucleus
Therefore, the density of the nucleus is
The volume occupied by the electrons is to be calculated. The volume of the electrons is calculated by measuring the amount of difference in the volume of the nucleus and the volume of the atom.
The volume of an atom is calculated as follows:
Conversion of the radius of pm into cm is as follows:
The volume of a sphere is
Here,
and
Substitute the values in the above equation:
Therefore, the volume of the atom calculated is
The volume of the electron is calculated by calculating the difference in the volume of the atom and the volume of the nucleus.
The volume of the electron is calculated as follows:
Substitute the values in the above equation:
Thus, the volume of the electron is
The mass consists of
Substitute the value in the above equation:
Therefore, the mass of
Now, the mass and volume of the electrons are calculated. The density of space occupied by an electron is to be calculated, which is as follows:
Substitute the value of the mass of electron
Therefore, the density of the electron is
Yes, the calculated result supports the Rutherford model of an atom. From the calculation, the space occupied by the electron is very less as compared to the space occupied by the nucleus of an atom. Therefore, it is proved that most of the space is empty, and the calculated density of the space occupied by the electrons also supports the Rutherford model of an atom.
Want to see more full solutions like this?
Chapter 2 Solutions
CHEMISTRY(LOOSELEAF W/CODE)- CUSTOM
- The photo here depicts what happens when a coil of magnesium ribbon and a few calcium chips are placed in water. (a) Based on these observations, what might you expect to see when barium, another Croup 2A element, is placed in water? (b) Give the period in which each element (Mg. Ca, and Ba) is found. What correlation do you think you might find between the reactivity of these elements and their positions in the periodic table?arrow_forwardThe early alchemists used to do an experiment in which water was boiled for several days in a sealed glass container. Eventually. some solid residue would appear in die bottom of the flask, which was interpreted to mean that some of the water in the flask had been converted into earth. When Lavoisier repeated this experiment, he found that the water weighed the same before and after heating, and the mass of die flask plus the solid residue equaled the original mass of the flask. Were the alchemists correct? Explain what really happened. (This experiment is described in the article by A. F. Scott in Scientific American, January 1984.)arrow_forwardWhich of these statements are qualitative? Which are quantitative? Explain your choice in each case. (a) Sodium is a silvery-white metal. (b) Aluminum melts at 660 C. (c) Carbon makes up about 23% of the human body by mass. (d) Pure carbon occurs in different forms: graphite, diamond, and fullerenes.arrow_forward
- (a) Assuming the dimensions of the nucleus and atomshown in Figure 2.10, what fraction of the volume of the atomis taken up by the nucleus? (b) Using the mass of the protonfrom Table 2.1 and assuming its diameter is 1.0 x 10-15 m,calculate the density of a proton in g/cm3.arrow_forwardWhat is the symbol of the element in Group 4A(14) and Period 2?arrow_forwardThe vitamin niacin (nicotinic acid, C6H5NO2) can be isolated from a variety of naturalsources such as liver, yeast, milk, and whole grain. It also can be synthesized fromcommercially available materials. From a nutritional point of view, which source ofnicotinic acid is best for use in a multivitamin tablet? Why?arrow_forward
- The anticancer drug Platinol (Cisplatin), Pt(NH₃)₂Cl₂,reacts with the cancer cell’s DNA and interferes with its growth.(a) What is the mass % of platinum (Pt) in Platinol? (b) If Pt costs$19/g, how many grams of Platinol can be made for $1.00 million(assume that the cost of Pt determines the cost of the drug)?arrow_forwardFor each of the following elements, write its chemical symbol,locate it in the periodic table, give its atomic number,and indicate whether it is a metal, metalloid, or nonmetal:(a) chromium, (b) helium, (c) phosphorus, (d) zinc, (e) magnesium,(f) bromine, (g) arsenic.arrow_forwardThe radius of a tantalum atom is 142 pm. How many tantalum atoms would have to be laid side by side to span a distance of 2.85 mm?arrow_forward
- If you wanted to make an accurate scale model of the hydrogen atom and decided that the nucleus would have a diameter of 1 mm, what would be the diameter of the entire model?arrow_forwardAn atom of rhodium (RhRh) has a diameter of about 2.7×10−8cm2.7×10−8cm. Part A: What is the radius of a rhodium atom in angstroms (ÅÅ)? Express your answer using two significant figures. Part B: What is the radius of a rhodium atom in meters (mm)? Express your answer using two significant figures. Part C: How many RhRh atoms would have to be placed side by side to span a distance of 2.0 μmμm ? Express your answer using two significant figures. Part D: If the atom is assumed to be a sphere, what is the volume in m3m3 of a single RhRh atom? Express your answer using two significant figures.arrow_forwardThe radius of a rhodium atom is 134 pm. How many rhodium atoms would have to be laid side by side to span a distance of 1.70 mm?arrow_forward
- Chemistry & Chemical ReactivityChemistryISBN:9781337399074Author:John C. Kotz, Paul M. Treichel, John Townsend, David TreichelPublisher:Cengage LearningChemistry & Chemical ReactivityChemistryISBN:9781133949640Author:John C. Kotz, Paul M. Treichel, John Townsend, David TreichelPublisher:Cengage LearningChemistryChemistryISBN:9781305957404Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCostePublisher:Cengage Learning
- Chemistry: The Molecular ScienceChemistryISBN:9781285199047Author:John W. Moore, Conrad L. StanitskiPublisher:Cengage LearningIntroductory Chemistry: A FoundationChemistryISBN:9781337399425Author:Steven S. Zumdahl, Donald J. DeCostePublisher:Cengage Learning