SAE 2.7 The density of the nucleus of a particular atom is 1 x 1013 g/cm³. Given that the diameter of a nucleus is 1 × 10-4 Å, estimate the mass of the nucleus, assuming it is a sphere. a. 1013 g b. 41889 g c. 4.19 x 10-23 g d. 5.23 x 10-24 g

Average Atomic Weight Part 1: Consider the four identical spheres below, each with a mass of 2.00 g. Calculate the average mass of a sphere in this sample. Part 2: Now consider a sample that consists of four spheres, each with a different mass: blue mass is 2.00 g, red mass is 1.75 g, green mass is 3.00 g, and yellow mass is 1.25 g. a Calculate the average mass of a sphere in this sample. b How does the average mass for a sphere in this sample compare with the average mass of the sample that consisted just of the blue spheres? How can such different samples have their averages turn out the way they did? Part 3: Consider two jars. One jar contains 100 blue spheres, and the other jar contains 25 each of red, blue, green, and yellow colors mixed together. a If you were to remove 50 blue spheres from the jar containing just the blue spheres, what would be the total mass of spheres left in the jar? (Note that the masses of the spheres are given in Part 2.) b If you were to remove 50 spheres from the jar containing the mixture (assume you get a representative distribution of colors), what would be the total mass of spheres left in the jar? c In the case of the mixture of spheres, does the average mass of the spheres necessarily represent the mass of an individual sphere in the sample? d If you had 80.0 grams of spheres from the blue sample, how many spheres would you have? e If you had 60.0 grams of spheres from the mixed-color sample, how many spheres would you have? What assumption did you make about your sample when performing this calculation? Part 4: Consider a sample that consists of three green spheres and one blue sphere. The green mass is 3.00 g, and the blue mass is 1.00 g. a Calculate the fractional abundance of each sphere in the sample. b Use the fractional abundance to calculate the average mass of the spheres in this sample. c How are the ideas developed in this Concept Exploration related to the atomic weights of the elements?

In a neutron star, gravity causes the electrons to combine with protons to form neutrons. A typical neutron star has a mass half that of the sun, compressed into a sphere of radius 20 km. If such a neutron star contains 6.01056 neutrons, calculate its density in grams per cubic centimeter. Compare this with the density inside a 232Th nucleus, in which 142 neutrons and 90 protons occupy a sphere of radius 9.11013cm . Take the mass of a neutron to be 1.6751024g and that of a proton to be 1.6731024g .

Uranium-235 is the isotope of uranium commonly used in nuclear power plants. How many (a) protons are in its nucleus? (b) neutrons are in its nucleus? (c) electrons are in a uranium atom?