PROBLEMS TO DO: Chapter 3 and 24
Directions: For review read pages 103 – 111 and answer questions 1-5. Read pages 112-117 before answering questions 6-8. 1. The nucleus of an aluminum atom has a diameter of about 2.0 x 10 -13 cm. The atom has an average diameter of about 3.0 x 10-8 cm. a. Calculate the ratio of the diameter of the atom to the diameter of the nucleus. b. 2. Calculate the ratio of the volume of the atom to the volume of the nucleus.
Assume that the nucleus of the fluorine atom is a sphere with a radius of 5.0 x 10-13 cm. Calculate the density of matter in the fluorine nucleus.
Use your periodic table to fill in all blank spaces in the following table. Atomic # of # of # of Mass ELEMENT # Protons Electrons Neutrons # Aluminum (Al) Beryllium (Be) Bismuth (Bi) Calcium (Ca) Carbon (C) Fluorine (F) Phosphorus (P) Iodine (I) 4. 15 53 6 9 16 127 83 20 20 6 19 13 4 27 9 209
Net Atomic Charge
Helium, as found in nature, consists of two isotopes. Most of the atoms have mass number of 4, but a few have mass number of 3. For each isotope, indicate the atomic number, number of protons, number of neutrons, mass number, and nuclear charge. How does the argon atom (atomic number 18, mass number 39) differ from the potassium atom (atomic number 19, mass number 39)? What changes in mass and atomic number result when an atom emits an alpha particle? beta particle?
7. Write the equation for the nuclear reactions which occur when each of the following nuclei emit alpha particles: a.
8. Write equations for the reactions which occur when each of the following emit beta particles: 238 244 3 185 93 Np a. b. 95 Am c. 66 Dy d. 1 H 9. Write equations for the nuclear reactions which occur when: a. Uranium-235 is bombarded by neutron and forms two new elements, barium-141 and Krypton-92. (Hint: Be sure mass numbers and atomic numbers balance.) b. Potassium-40 is bombarded by an electron to form a new element. 10. Radioactive atoms of astatine-216 undergo a series of three spontaneous nuclear reactions before changing into stable atoms. These changes are: (a) the atom disintegrates into an alpha particle and a second radioactive atom; (b) the second radioactive atom disintegrates into an alpha particle and a third radioactive atom; (c) this third atom then disintegrates into a beta particle and a stable atom which disintegrates no more. Write three balanced nuclear equations for the changes involved. 11. If radioactive wastes must be stored for seven half-lives before disposal: a. how long must P-32 be held? (half-life is 14.3 days) b. what fraction of the P-32 originally set aside remains after this time? 12. Uranium-228 has a half-life of 10 minutes and undergoes alpha (α) emission when it decays. a. Write the nuclear equation for the decay of U-228. b. If you had a 1.00 g sample, how many grams of U-228 would you have after 10 minutes; after 20 minutes; after one hour? c. For each of the above cases, calculate the number of individual atoms that would be left. 13. Naturally occurring chlorine is composed of 75.402% chlorine-35, and 24.60% chlorine-37. What is the weight of a mole of "average" atoms in a mixture of the above samples? Compare your answer to the atomic weight found on the periodic table. Note that atomic weights are the average weights of a mole of naturally occurring isotopes. Be sure to pay close attention to significant figures in this calculation.
FOR MORE PRACTICE 1. An average dimension for the radius of a nucleus is 1.0 X 10-12 cm and for the radius of an atom, 1.0 x 10-8 cm. Determine the ratio of atomic volume to nuclear volume. 2. Suppose a copper atom is thought of as occupying a sphere 2.6 x 10-8 cm in diameter. If a spherical model of the copper atom is made with a 5.2 cm diameter, how much of an enlargement is this? 3. Radioactive element A with mass 220 and atomic number 85 emits an alpha particle and changes to element B. Element B emits a beta particle and is converted to element C. What are the atomic masses and atomic numbers of elements B and C? 4. Write a nuclear equation for the emission of an alpha particle by 5. Write the nuclear equation for the emission of a beta particle by
6. Write equations for the reactions which occur when: a. Tin-113 is bombarded by a beta particle to form a new element. b. Nitrogen-14 is bombarded by an alpha particle to form a proton and a new element. 7. Write the nuclear equations for the successive emissions of an alpha particle and a beta 214 particle form 84 Po . 8. Bismuth-210 has a half-life of 5 days, undergoes beta (β) emission. a. Write the nuclear equation for the decay of Bi-210. b. If you had 5g sample, how much Bi-210 would you have after 10 days; after 5 weeks, after 70 days? c. For each case above, calculate the number of individual atoms that would be left. CAN YOU ACCEPT A CHALLENGE 1. How many electrons would be required to weigh 1.00 G? What would be the weight of one mole of electrons? (1 electron weighs 9.11 x 10-28g) Describe the spectrum produced on a photographic plate in a mass spectrograph if a mixture of the isotopes of oxygen (16O, 17O, 18O) is analyzed. Consider only the record for +1 and +2 ions. Hydroxylamine(NH2OH) is subjected to electron bombardment. The products are passed through a mass spectrograph. The two pairs of lines formed indicated charge/mass ratios of 0.0625, 0.0588, and 0.1250 and 0.1176. How can this be interpreted?