The Shell Model This activity is modified from Chemistry: A Guided Inquiry (3/e) by R.S. Moog and J.J. Farrell, Wiley, 2006. The first ionization energy (IE 1 ) is the minimum energy required to remove the first electron from a gaseous atom of an element, M. M(g) M+(g) + e - Q1) Based on your knowledge that He is more stable than H, which has a higher IE, He or H? (HINT: Which is harder to remove electrons from, H or He?) Model 1: The Shell Model for Hydrogen: nucleus +1 electron Q2) Hydrogen (above) has an ionization energy of 1.31 MJ/mol. a) Does the ionization energy increase or decrease if the electron is farther from the nucleus? (Hint: Is it easier or harder to remove the electron?) +1 b) Does the ionization energy increase or decrease if the electron is in the first orbit, but the nucleus is twice as positive? (Hint: Is it easier or harder to remove the electron?) +2 Page 1 of 6
Q3) Model A and B are shown below. Is the ionization energy of all electrons in Model A the same? Is the ionization energy of all electrons in Model B the same? Model A) Model B) +2 +2 Q4) Helium contains two electrons. 2.37 MJ/mol of helium atoms can be used to ionize either of the two electrons. Which of the models (A or B) is the best model for Helium? Q5) Explain why the ionization energy of He (2.37 MJ/mol) is almost twice that of H 1.31 MJ/mol). Use the Model you chose in Q4 to help you explain this. Q6) a) For lithium (which has 3 electrons), fill in the 2 electrons first (as it should be in Helium, see Q3-4 above). +3 b) The ionization energy of lithium is 0.52 MJ/mol! (Compared to H at 1.31 and He at 2.37 MJ/mol) Where should the third electron go? Draw it into the diagram and explain your choice. Page 2 of 6
Without knowing it you have been using the shell model! (Orbits, as in the Bohr model). You have seen that hydrogen and helium have electrons that occupy the first shell (n=1) and lithium has electrons occupying the first and second shells (n=1, 2). Model 2 Core Charge Concept Valence electrons (Outer shell) Core electrons (Inner shell) +3 +1 Shell Model Core Charge Concept (Valence electron feels +1) In the shell model, the inner (core) electrons shield the charge so the outer (valence) electron does not feel the full effective nuclear charge. (It s almost as if the two inner electrons neutralize the nucleus for the third electron). The effective nuclear charge is approximated by using the core charge concept. Q7) a) What is the number of valence electrons in H, He, and Li? (Based on Model 1, Q1-6) b) What is the number of core electrons in H, He, and Li? c) What is the core charge of H, He, and Li? Q8) Apply the shell model and core charge concept to Beryllium (Be). If the ionization energy of Be is 0.90 MJ/mol (compared to 0.52 MJ/mol for Li), should the fourth electron go in the second or the third shell? Fill it into the diagram below. (Hint: Is it easier or harder to remove this electron, based on the ionization energies given? How far from the nucleus should it be?) +4 Page 3 of 6
Q8) continued a) Why is the nuclear charge of Be +4? b) What is the number of core electrons? c) What is the number of valence electrons? d) What should the core charge be? e) What is the relationship of core charge to the number of valence electrons? Q9) Briefly explain how the core charges of Li and Be are consistent with their IE values (0.52 MJ/mol for Li versus 0.90 MJ/mol for Be). Table 1: First ionization energies of the first 20 elements Z atomic # Element Ionization Energy (MJ/mol) Z atomic # Element Ionization Energy (MJ/mol) 1 H 1.31 11 Na 0.50 2 He 2.37 12 Mg 0.74 3 Li 0.52 13 Al 0.58 4 Be 0.90 14 Si 0.79 5 B 0.80 15 P 1.01 6 C 1.09 16 S 1.00 7 N 1.40 17 Cl 1.25 8 O 1.31 18 Ar 1.52 9 F 1.68 19 K 0.42 10 Ne 2.08 20 Ca 0.59 Q10) We saw in Q3,Q4 that the first shell is full for He. Which element after He has a filled second shell, based on the ionization energies given in Table 1? Explain your choice. Q11) Based on Q10, what is the maximum number of electrons that can go in the second shell? (Just the second shell, not including the first shell)? Look for trends in the data. Page 4 of 6
Q12) Draw a picture of Neon based on your answers to Q10, 11 using both the shell model and the core charge concept. (2 drawings) Q13) The element after Neon is Sodium (Na). Sodium has one more electron than neon. In which shell does this electron go? Briefly explain. (See ionization energy) Table 2 : Data for some selected elements Element Valence Shell (n) # of Valence Electrons Core Charge Ionization Energy (MJ/mol) H 1 1 1.37 Li 2 1 0.52 Na 3 1 0.50 Rb F 2 7 1.68 Cl 3 7 1.25 Q14) a) Complete the column for core charge. b) What is the relationship of the core charge and the number of valence electrons in these atoms and their position in the periodic table? c) What I the relationship of the valence shell (n) of these atoms to their position in the periodic table? d) Predict values for Rb. e) Briefly explain how the ionization energy of Rb is lower than the ionization energy for the elements above it in Table 2. (HINT: Is it easier or harder to remove an electron from Rb? Why?) Page 5 of 6
Q15) How does the core charge of an atom change as you move left to right (across the periodic table)? Q16) a) Based on the trend in Q15, should the ionization energy increase or decrease as you move left to right (across the periodic table)? Explain. b) Is this observed in Table 2? Exercises This material is not covered in your textbook. A reference material will be placed on the website if you need assistance with this material. 1. Explain why the ionization energy data is not consistent with Na having nine electrons in its second shell. 2. How many electrons does Na have in shell n=1? n=2? n=3? 3. Based on the ionization energy data, is the radius of the valence shell in Na larger or smaller than that of Li? Explain. 4. For each of the elements C, O, N, and Ne: a) sketch a shell model and a core concept model; b) find the number of valence electrons; c) what is the core charge? 5. Which electrons are harder to remove in a given atom, valence electrons or core electrons? Explain. 6. Indicate whether the following are true or false and explain your reasoning: a) The core charge of Br is +7 b) Helium has the largest first ionization energy 7. If a single electron is removed from a lithium atom, the resulting Li+ cation has only two electrons both in the first shell. How would you expect the ionization energy of a lithium cation to compare to that of a helium atom? Explain your reasoning. (HINT: Diagram both, and consider their differences). Page 6 of 6