Discussion Today For One-electron Atoms

Discussion #12 Things you should know when you leave Discussion today for one-electron atoms:    e ΔEmatter=En-Em ; Ionization Energy(IE)=E∞ – En(initial) ΔΕlight = hνlight = IE + KE f. 1. Consider the following energy levels of the hydrogen atom as shown below in the diagram: a. Sketch electron clouds corresponding to energy levels up to n = 3: What is the ground state H atom ionization energy in J, eV and kJ/mol? H(g)  H+(g) + e- b. When electron cloud of the H atom at the lowest energy interacts with light of the lowest resonate frequency, sketch the resulting electron cloud(s): c. When electron cloud of the H atom at the lowest energy interacts with light of the 2nd lowest resonate frequency, sketch the resulting electron cloud(s): d. When electron cloud of the He atom at the lowest energy interacts with light of the lowest resonate frequency, sketch the resulting electron cloud(s): e. What are the two energy levels involved in the ionization energy of an electron from H in the ground state? g. What is the expression for the ionization energy of an electron from the n = 3 state of a one electron atom with atomic number Z? 2. Hypothetical atom, X, has the following ground state absorption spectrum displayed below, and the ground state ionization energy of the atom is 15 eV (IE). Each of the absorption lines corresponds to a natural frequency of the electron cloud resulting from the mixing of electron wave with 1 loop with electron wave with more than one loop (i.e. the atom always starts in its ground state during each absorption). In answering the following questions, assume that the zero of energy is the ionized atom X  X+ + e- a. What is the energy of the ground state (of the electron cloud corresponding to one loop) of X? Hint: pay attention to the sign b. Construct the energy level diagram for X. Hint: How many energy levels are necessary to account for the absorption spectrum? c. Using the energy level diagram you just drew: How many emissions are possible in the electrically-excited emission spectrum of this atom? d. What is the energy of the third excited state of X? How many loops does that state have? e. What is the energy of the highest energy state of X that is necessary to account for the absorption spectrum? f. Is it possible for an electron in the ground state of atom X to absorb light of energy 3 eV or will it be transparent to it? 2 g. Can atom X emit light of energy 3 eV? h. Is it possible for X to absorb light of energy 16 eV or will it be transparent to it? Why? i. Can atom X emit light of energy16 eV? j. What is the lowest frequency of the light emitted from the atom? k. Draw the emission spectrum: l. At home: Calculate the kinetic energy of an electron (in Joules) that was ionized by light of frequency of 5∙1015 Hz from the ground state. Hint: Remember that energy must be conserved. (1.6021766 10-19 J = 1 eV) 3. What is the expression for the energy (in J) for the ground state of an electron cloud in Li2+? a. Calculate wavelength (in nm) of the light corresponding to the Li2+ electron cloud resulting from mixing a 3 loop electron wave with a 1 loop electron wave? 4. Photons of energy 13.6 eV = Ry are able to ionize H in its n = 1 energy level. Are photons of this energy are able to ionize He+ in its n = 2 energy level? 5. The photoelectric effect threshold frequency of a metal is υ0 = 1 1015 Hz. Gamma radiation of frequency 1 1017 Hz ejects electrons from the metal. Which of the following occurs when the intensity of the gamma radiation is reduced by 50.%? a. b. c. d. e. f. The velocity of the ejected electrons will be reduced by a factor of two. The kinetic energy of the ejected electrons will be reduced by a factor of two. The kinetic energy of the ejected electrons will be reduced by a factor of four. Kinetic energy and the velocity of the ejected electrons will stay the same. Number of ejected electrons will increase. Number of ejected electrons will decrease. 6. Assume light is able to eject electrons from a metal. What do you expect as the wavelength of the light is increased? a. If the light wavelength reaches the lowest, electrons will no longer be ejected. 3 b. Electrons will still be ejected but they will move faster and faster. c. Electrons will still be ejected but they will move slower and slower. d. More and more electrons will be ejected but they will have the same kinetic energy. e. More information needed. 7. One atom emits light of energy 1.27 eV. A second atom has only three energy levels: -0.9 eV, -1.27 eV, and -1.9 eV. Assuming ionization is not possible can the second atom absorb the light emitted by the first atom. 8. For the two hydrogen electron clouds below identify the quantum number “n”, the quantum number “l”, the number of radial loops “j”, and the specific name of the orbital you must indicate orientation, e.g. 3dxy). A B z n= x l= j= z n= l= j= x y name:_________________ name: a. For the two hydrogen electron clouds above, which has the largest ionization energy? Note: in H atom, all orbital of the same n have the same energy. 9. What are the possible angular momentum quantum numbers for an orbital in the n=4 shell? a. How many degenerate orbitals are in the n=3 shell? What are they? Note: in H atom, all orbitals of the same n have the same energy. 10. The figure shows three H atom electron clouds. a. Which of the following H atom electron clouds has the largest ionization energy? b. Write down the numerical expression that when evaluated gives the value in eV of smallest ionization energy of these three clouds. A B C Things you should know when you leave Discussion today for multi-electron atoms:  Many electron system Mahaffy, 2e section 8.4  Electron configurations Mahaffy, 2e section 8.5 4  Shielding and effective nuclear charge: Mahaffy, 2e section 8.6 o e  Periodicity: Mahaffy, 2e section 8.7 1. Below is a plot of the first 10 ionization energies for a single atom in 3rd row of the periodic table. The x-axis shows which ionization (e.g. IE1, IE2, etc.) and the y-axis gives how much energy in (MJ/mol). a. What 3rd row element does the plot show? b. First ionization energy IE1 is 10.36 eV calculate Zeff for that element. Note: We will not use Slater’s rules for eff, so please ignore Mahaffy et al., section 8.6, pages 289 to 291.(Useful information: 1eV = 1.6021766 10-19 J; A = 6.022140857 × 1023/mol) IE= E∞ - Einitial= = e c. The arrow points to the jump between the 6th and 7th ionization energy. Which of the following statements are true? i. The number of protons (Z) changed. ii. The effective nuclear charge (Zeff) changed. iii. The quantum number n of the electron that is ionized changed. iv. The radius of the ion decreased Ionization Energy (MJ/mol) 50 40 30 20 10 0 0 1 2 3 4 5 6 7 8 9 10 11 # of Electrons Ionized 2. From the following three different neutral atoms electron configurations, label the one with the highest third ionization energy, and lowest third ionization energy. Explain your 5 answers. Hint: remember that number of electrons in the neutral atom equals the number of protons. a. 1s2 2s2 2p6 3s2 3p6 4s2 b. 1s2 2s2 2p6 3s2 3p6 4s1 c.1s2 2s2 2p6 3s2 3p6 3. Which one will have the greatest ionization energy: Na+, Ne, F-, O2-? 4. Answer the following questions about manganese (Mn): a. What is the electron configuration? b. First ionization energy IE1 is 7.43 eV calculate Zeff for that element. c. Circle the letters corresponding to the picture of occupied electron clouds. Hint: you need to know what are n, l, and j for one electron in each of the occupied electron clouds. A B C D E F For the pictures G H I above, fill in the empty boxes on the graphs on the next page with corresponding names of the orbitals (1s, 2s, 3s, 4s, 2p, 3p, 3d): 6 0.6 0.5 0.4 0.3 0.2 0.1 0 0.25 0.2 Probability Probability d. Use the radial probability densities on the next page (electron cloud cross section below) to estimate the size of an atom of Mn. Hint: Look at the x axis. 0.15 0.1 0.05 0 0 2 4 0 5 0.07 0.12 0.06 0.1 0.05 0.04 0.03 0.02 0.08 0.06 0.04 0.02 0.01 0 0 0 10 20 30 0 Distance from Nucleus (Angstroms) 5 10 15 20 Distance from Nucleus (Angstroms) 0.25 0.12 0.2 0.1 Probability Probability 10 Distance from Nucleus (Angstroms) Probability Probability Distance from Nucleus (Angstroms) 0.15 0.1 0.05 0.08 0.06 0.04 0.02 0 0 0 2 4 6 8 10 0 Distance from Nucleus (Angstroms) 5 10 15 20 Distance from Nucleus (Angstroms) Additional Practice Problems 0.12 0.1 Probability 1. What electron the line wavelength 434 spectrum for atoms? (In the the emission natural cloud resulting electron wave with the 0.08 0.06 0.04 0.02 0 0 5 10 15 Distance from Nucleus (Angstroms) 7 20 cloud energies account for corresponding to the nm in the gas discharge the Balmer series of H Balmer series in each of lines corresponds to a frequency of the electron from the mixing of an with more than two loop electron wave with 2 loop) A. B. C. D. E. F. Only the n = 3 cloud energy Only the n = 4 cloud energy Only the n = 5 cloud energy The n = 2 and n = 4 cloud energies The n = 2 and n = 5 cloud energies None of these. 2. The ionization wavelength of H atom in the n = 2 energy level is 365 nm. Will light of this wavelength ionize He+ in the n = 1 level? 3. The light with wavelength of 365 nm will ionize H atom in the n = 2 energy level. What effect will light with wavelength 657 nm have? (Choose all that apply.) a. Atom will be transparent to the light of this wavelength b. Ionization will take place c. Ionization will not take place d. The ionized electron will use excess energy for kinetic energy 4. The light with wavelength of 365 nm will ionize H atom in the n = 2 energy level. What effect will light with wavelength 265 nm have? (Choose all that apply.) a. Atom will be transparent to the light of this wavelength b. Ionization will take place c. Ionization will not take place d. The ionized electron will use excess energy for kinetic energy 5. An electron is ionized from the ground state of an atom, with E1 = –30 eV, by light for which a photon of light energy is 36 eV. What is the kinetic energy (in eV) of the ejected electron? 6. What is kinetic energy of the electron ionized from Li2+ in its n = 6 level by light of wavelength 310 nm? 7. In terms of the variables (i.e. Ry, h, and c) what is the smallest possible wavelength of light that will be emitted by a He+ atom starting with the energy corresponding to 6 loops? 8. What is the largest possible wavelength of light that will be emitted by be the Li2+ atom with the energy level corresponding to 6 loops. 9. An electron is ionized from the ground state of an atom, with E1 = -1.3·10-19 J, by light with frequency 1.0·1015 Hz. What is the kinetic energy (in eV) of the ejected electron? -19 J. 10. The work function ionization energy , of chromium metal is a. What is the maximum kinetic energy of an electron, if it is ejected from chromium metal by light of wavelength 250. nm? b. What will happen to the speed and quantity of the ejected electrons if the wavelength of the light will increase? c. What will happen to the speed and quantity of the ejected electrons if the wavelength of the light will decrease? 8 d. What will happen to the speed and quantity of electrons if the intensity of the light will increase? 11. An atom has only three energy levels, -2.5, -4.0, and -4.5 eV. Draw the absorption spectrum for a gas of these atoms excited by an electric discharge. Hint: you need to draw energy level diagrams to answer this question assume the most negative energy is an energy of the ground state a. Draw the emission spectrum. Hint: does it always just go to the ground state? 12. An atom has only three energy levels, -2.6, -4.1, and -5 eV. Draw the absorption spectrum for a gas of these atoms excited by an electric discharge. a. List all the lines in the emission spectrum. Do not assume that it always goes to the ground state. 13. An atom has energy levels of -2.2∙10–18 J, -5.5∙10–19 J, -2.5∙10–19 J, -1.4∙10–19 J, -8.7∙10–20 J, and -6.1∙10–20 J. a. Calculate the λ in nm of light that is necessary to excite an electron to E∞ from E2. b. What is the λ in nm of light necessary to excite an electron to E3 from E2? c. How many emission lines (in total) are possible for an atom with these energy levels? d. How many ground-state absorption lines are possible for an atom with these energy levels? 14. Draw the electron configuration diagram for C, but fill the diagram as if the C is in the ground state. Draw a dotted line around a shell. Circle a subshell. Draw a triangle around an orbital. Is C atom paramagnetic or diamagnetic? a. Calculate Zeff of C, if IE1 = 1086 kJ/mol. (Hint: IE= E∞-Einitial 15. Rank the following in terms of increasing ionization energy: Na, Li, B, N, Ne 16. Rank the following in terms of increasing ionization energy: Li+, B+, N+, Ne+, Na+ 17. Write the ground state electron configuration for the following atoms and ions and determine if each is paramagnetic or diamagnetic: Al, Al3+, V, V3+ 9 ) Trends in IE1 is explained by: a. Z increases b. Electron –electron repulsion c. New shell d. l increases or Zeff decreases (shielding) IE1 Ions (Ions Electron configuration) Atom Z Electron configuration He 2 1s 2 2373 He+ 1s 1 Li 3 1s22s1 520 Li+ 1s 2 Be 4 1s22s2 899 Be+ 1s22s1 B 5 _________________ 801 C 6 N 7 ________________ 1400 O 8 ________________ 1314 F 9 Ne 10 ________________ 2080 Na 11 ________________ 496 Mg 12 Al 13 Zeff B+ ________________ C+ 1086 N+ O+ F+ 1680 = e e ________________ Ne+ Na+ Mg+ 738 e Al+ 578 e 10 IE2 Atom Z Electron configuration He 2 He+ 1s1 Li 3 Li+ 1s2 7300 Be 4 Be+ 1s22s1 1757 B 5 C 6 N 7 O 8 F 9 Ne 10 Na 11 12 Mg B+ C+ N+ O+ F+ Ne+ Na+ Mg+ e Zeff 5248 2430 2350 2860 3390 3370 3950 4560 1450 Al+ Al 13 1820 e 11 Trends in IE2 is explained by: a. Z increases b. Electron –electron repulsion c. New shell d. l increases or Zeff decreases (shielding) Handout Answers: 1. ds a. n=1 n=2 n=3  b.  c. d. e. n and n ∞ -18 J = 13.6eV = 1312 f. IE = g. IE = Ry 2. a. b. c. d. e. f. g. h. i. j. k. l. -15 eV 6 15 emissions -8 eV, 4 loops -3 eV, 6 loops No Yes Yes no 2.4*1014Hz (10 lines) KE=910-19 J Additional Practice Problems: 1. E 2. No 3. A, c 4. B, D 5. 6eV 6. 0.94*10-19 J 7. =9hc/35Ry 8. 3. -9Ry a. 11.36 nm 4. Yes 5. D,F 6. C 7. No 8. 4dzx, 4py a. The same 9. 0,1,2,3 10. 2s, 4p, 3d a. 2s b. 0.85 (n4 to n∞)  100hc 11Ry 9. 3.3eV 10. a. 7.510-20 J b. Speed decreases, number will still the same c. Speed increases, number of electrons will stay the same d. Speed stays the same, number of electrons will increas 13. a. 361 nm b. 662 nm c. 15 lines d. 5 lines 14. Zeff = 1.82 15. Na < Li < B < N < Ne 16. B+ < N+ < Ne+ < Na+ < Li+ 17. Al: 1s2 2s2 2p6 3s2 3p1 paramagnetic Al3+: 1s2 2s2 2p6 3s0 3p0diamagnetic V: 1s2 2s2 2p6 3s2 3p6 4s2 3d3 paramagnetic V3+: 1s2 2s2 2p6 3s2 3p6 4s0 3d2 paramagnetic Many Electrons Atoms: 1. a. Sulfur b. ii, iii, iv 2. a – highest, c – lowest 3. Na+ 4. a. [Ar] 4s2 3d5 b. All except C & F c. Left column: 1s, 4s, 2p; Right column: 2s, 3s, 3p; Bottom: 3d d. ≈ Å 12 Atom He Li Z Electron configuration B C N O F Ne Na Mg Al Zeff kJ mol 1s2 2373 1s22s1 520 2 Trends in IE1 is Explained by: e. Z increases f. Electron –electron repulsion g. New shell h. l increases or Zeff decreases (shielding) 899 1.26 6 7 8 9 10 11 12 13 IE2 He+ 1s1 5248 c, d 7300 Li 1s2 1757 + Be 1s22s1 a,b 1s 2 2s 2 2 p1x 801 1s 2 2s 2 2 p 1x 2 p 1y 1086 1s 2 2 s 2 2 p 1x 2 p 1y 2 p 1z 1400 1s 2 2 s 2 2 p x2 2 p 1y 2 p 1z B+ 1.56 2430 d 1.82 2350 C+ 1s 2 2s 2 2 p1x a 2860 2.07 a 1314 1680 1s 2 2 s 2 2 p x2 2 p y2 2 p z2 2080 + N 1s 2s 2 p 1x 2 p 1y 2 2 2.00 3390 b 1s 2 2 s 2 2 p x2 2 p y2 2 p 1z + O 1s 2 s 2 p 1x 2 p 1y 2 p 1z 2 2 F+ 2.26 3370 a 2.52 3950 a,b 1s 2 2 s 2 2 p x2 2 p y2 2 p z2 3s 1 496 1.86 1s 2 2s 2 2 p x2 2 p y2 2 p z2 3s 2 738 c, d 2.25 Ne 1s 2 s 2 p x2 2 p y2 2 p 1z 2 2 + Na 1s 2 2 s 2 2 p x2 2 p y2 2 p z2 1450 a  [ Ne]3s 2 578 + 4560  [ Ne]3s1 [ Ne]3s 2 3 p1x kJ mol + 1.66 4 5 Ions (Ions Electron configuration) a 1.35 3 1s22s2 Be IE1 + Mg [ Ne]3s1 1820 1.99 d 13 + Al [ Ne]3s 2 Exam 3 Answers: 4.6kJ 12C(s, graphite) +11H2(g) +11/2 O2(g)  C12H22O11( ) 6C(s, graphite) +9H2(g) +3/2 O2(g)  CH3CH2OH( ) Cc a. -57.05 kJ/mol b. 228.2 kJ/mol c. -10.86kJ 5. -694 kJ/mol 6. -6 kJ/mol 7. a. 1.81*10-10s b. 656nm c. -276Kj 8. < 0; > 0; < 0; > 0; (const. pressure) < 9. 3,4,2 0,2,1 3s,4d,2p 1,5,3 B 10. 23.2°C 11. 0J 12. F,F,T,F,F 13. 37.4 kJ/mol 1. 2. 3. 4. 14 (const. volume)