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Unformatted text preview: CHAPTER 30 THE NATURE OF THE ATOM ANSWERS TO FOCUS ON CONCEPTS QUESTIONS 1. (d) The Bohr model deals with a single negatively charged electron in orbit about a positively charged nucleus. Since only one electron is assumed to be present, the model does not take into account the electrostatic repulsion between electrons that would exist in a multiple- electron atom, such as helium (two electrons). 2. (c) According to Equation 30.10, the radius r n of an orbit is proportional to the square of the quantum number n . An increase in the radius by a factor of four, therefore, means that n has doubled. According to Equation 30.8, the magnitude L n of the orbital angular momentum is proportional to n . This means that L n doubles when r n doubles. 3. (b) The shortest wavelength shortest in a given series can be calculated from Equation 30.14 (with 2 i 1 n = ) as 2 2 shortest f 1 RZ n = , where R is the Rydberg constant and Z is the number of protons in the nucleus. 4. 1282 nm 5. (e) To remove an electron completely from an atom and place it at rest infinitely far from the nucleus of the atom, energy must be supplied in the amount of the ionization energy. 6. (e) In the quantum mechanical picture, the principal quantum number n can have the values 1, 2, 3, . The orbital quantum number can have the values ( 29 0, 1, 2, ..., 1 n =- . Thus, for n = 3, the possible values for are 0, 1, and 2. 7. (a) According to Equation 30.15, the magnitude L of the orbital angular momentum is ( 29 1 2 h L = + . This expression can be solved for , the orbital angular momentum quantum number, with the result that = 4. Since can be at most n 1, the principal quantum number n must be 5 or larger. Of the options given in this case, 5 is the only feasible answer. 8. (c) The spin angular momentum of the electron plays no role in the Bohr model, but it does play a role in the quantum mechanical picture. 9. 6.33 10 34 Js 9 THE NATURE OF THE ATOM 10. (e) The Pauli exclusion principle states that no two electrons in an atom can have the same set of the four quantum numbers n , , m , and m s . 11. (a) A subshell can contain up to a maximum of 2(2 + 1) electrons, where is the orbital quantum number. For the 5f subshell, = 3, so the maximum number of electrons is 2(2 + 1) = 14. For the 6h subshell, = 5, so the maximum number of electrons is 2(2 + 1) = 22. Therefore, 19 electrons can fit into the 6h subshell but not the 5f subshell. 12. (c) The maximum number is obtained by adding the maximum number for each subshell within the n = 5 shell. The value of the orbital quantum number defines a subshell, and for n = 5, the possible values for are 0, 1, 2, 3, and 4. Each subshell can contain up to a maximum of 2(2 + 1) electrons. Thus, the = 0 subshell can hold 2 electrons, the = 1 subshell can hold 6 electrons, the = 2 subshell can hold 10 electrons, the = 3 subshell can hold 14 electrons, and the...
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