Chapter 23 Problems 1, 2 , 3 = straightforward, intermediate, challenging Section 23.1 Properties of Electric Charges 1. (a) Find to three significant digits the charge and the mass of an ionized hydrogen atom, represented as H + . Suggestion: Begin by looking up the mass of a neutral atom on the periodic table of the elements. (b) Find the charge and the mass of Na + , a singly ionized sodium atom. (c) Find the charge and the average mass of a chloride ion Cl – that joins with the Na + to make one molecule of table salt. (d) Find the charge and the mass of Ca + + = Ca 2+ , a doubly ionized calcium atom. (e) You can model the center of an ammonia molecule as an N 3– ion. Find its charge and mass. (f) The plasma in a hot star contains quadruply ionized nitrogen atoms, N 4+ . Find their charge and mass. (g) Find the charge and the mass of the nucleus of a nitrogen atom. (h) Find the charge and the mass of the molecular ion H 2 O – . 2. (a) Calculate the number of electrons in a small, electrically neutral silver pin that has a mass of 10.0 g. Silver has 47 electrons per atom, and its molar mass is 107.87 g/mol. (b) Electrons are added to the pin until the net negative charge is 1.00 mC. How many electrons are added for every 10 9 electrons already present? Section 23.2 Charging Objects by Induction Section 23.3 Coulomb’s Law 3. The Nobel laureate Richard Feynman once said that if two persons stood at arm’s length from each other and each person had 1% more electrons than protons, the force of repulsion between them would be enough to lift a “weight” equal to that of the entire Earth. Carry out an order-of-magnitude calculation to substantiate this assertion. 4. Two protons in an atomic nucleus are typically separated by a distance of 2 × 10 –15 m. The electric repulsion force between the protons is huge, but the attractive nuclear force is even stronger and keeps the nucleus from bursting apart. What is the magnitude of the electric force between two protons separated by 2.00 × 10 –15 m? 5. (a) Two protons in a molecule are separated by 3.80 × 10 –10 m. Find the electric force exerted by one proton on the other. (b) How does the magnitude of this force compare to the magnitude of the gravitational force between the two protons? (c) What If? What must be the charge- to-mass ratio of a particle if the magnitude of the gravitational force between two of these particles equals the magnitude of electric force between them? 6 . Two small silver spheres, each with a mass of 10.0 g, are separated by 1.00 m. Calculate the fraction of the electrons in one sphere that must be transferred to the other in order to produce an attractive force of 1.00 × 10 4 N (about 1 ton) between the spheres. (The number of electrons
per atom of silver is 47, and the number of atoms per gram is Avogadro’s number divided by the molar mass of silver, 107.87 g/mol.) 7 . Three point charges are located at the corners of an equilateral triangle as shown in Figure P23.7. Calculate the resultant electric force on the 7.00- μ C charge.
- Winter '13