Learning Objectives Energy: Light as energy Describe the wave nature of light, wavelength, and frequency using the equation c = λν What is meant by the particle nature of light? Calculate the energy of a photon using the equation E = hν Be familiar with types of radiation and their relative energies in the electromagnetic spectrum (Which have long wavelengths? Which have short? Which have high energy, which have low?) Describe the relationship between color of visible light and its relative energy in the electromagnetic spectrum Describe the relationship between wavelength and energy of a photon using the equation E = hc/λ Perform calculations involving the total energy of multiple photons using the equation E T = n(hc/λ) Interpretation of Line spectrum (What is happening that causes the emission lines?) Know that quantized emissions represent energy transitions Be able to interpret line spectra by assigning lines to transitions Connect line spectra to the energy of emitted photons, the color of light emitted, and its wavelength Bohr Model of the hydrogen atom: where is the electron in the H atom? Qualitative Goals: Connect the line spectrum of hydrogen to the energy level diagram of hydrogen using the Bohr model. Define and describe the energy of an electron in the hydrogen atom Connect emission and absorption to pictures of electrons in orbit; We are using He + ion for this goal Have a qualitative ability to describe emission and absorption using the principal quantum number. Know the sign of the energy change (positive or negative) when emission or absorption occurs. Quantitative Goals Calculate E given n i and n f (Calculate energy of emitted photon.) Calculate ionization energy for H atom or He + (knowing that n = for ionization) Know that the energy change is negative if the photon is emitted. Orbitals: Solutions to Schrödinger equation What is meant by the electron density (or the probability of finding an electron)? Know the qualitative meaning of wavefunctions, which are solutions to the Schrödinger Equation. Describe the meaning of probability density, and electron density as the location of an electron. Quantum Numbers Be familiar with the names of principle, angular, and magnetic quantum numbers Define shell, subshell and orbital Know and follow rules for allowed combination of quantum numbers Understand the relationship between quantum numbers and size, shape, and orientation of an orbital Know orbital names. Describe the value of electron density in regions of space using electron density plots or contour diagrams Interpret an electron density plot, and define nodes and lobes of orbitals Make connections between electron configuration and orbitals; know that quantum numbers describe orbitals, and orbitals sufficiently describe the location of the electron Week 2 CHEM 110 -Fall 2013 30
Homework Problems Due: Thurs. Sept. 12 1. A radio station broadcasts on a frequency of 99.5 kilocycles/s. What is the wavelength of this radiation in km? A. 7.25 10 3 km B. 2.99 10 7 km C. 2.99 10 4 km D. 3.02 km E. none of these 2. A particular microwave photon has a wavelength of 0.01 m, a photon of green visible light has a wavelength of 520 nm and a photon of gamma radiation has a wavelength of 8 pm. Rank these forms of electromagnetic radiation in order of increasing energy and frequency. What general trend do you see? 3. How much energy does one mole of red photons have? (The wavelength of red light is 725 nm.) A. 2.74 10 19 kj B. 4.56 10 46 kj C. 6.05 10 3 kj D. 165 kj E. 227 kj 4. A He-Ne laser (λ = 633nm) is used to heat up a sample. How many photons are needed to transfer 12 J of heat to the sample? A. 3.8 10 19 B. 12,000 C. 6.3 10 11 D. 3.2 10 19 E. 1.6 10 6 5. The brightest emission line in the line spectrum of potassium is at 535nm. What is the energy of the photon emitted? 6. The brightest emission line of an element is 420nm. What is the color of the flame? A. red B. yellow C. green D. blue E. violet 7. Green light of wavelength 516 nm is absorbed by an atomic gas. What is the energy difference between the two quantum states involved in the transition? A. 5.81 10 14 J B. 3.85 10 19 J C. 1.28 10 27 J D. 4.29 10 36 J E. 1.43 10 44 J 8. Which of the following statements is/are true for the Bohr model of the hydrogen atom? 1. The radius of the orbit increases as the principal quantum number increases. 2. The energy required to ionize the atom increases as the principal quantum number decreases. 3. Light emitted by the excited hydrogen atom corresponds to transitions from orbits of higher principal quantum number to lower principal quantum number. A. 1 only B. 1and 2 only C. 2 and 3 only D. 1 and 3 only E. 1, 2, and 3 Week 2 CHEM 110 -Fall 2013 31
9. In the Bohr model for the hydrogen atom, in which orbit does an electron have higher overall energy: n = 1 or n = 5? 10. Which of the following transitions in a hydrogen atom results in emission of light? i. n = 3 to n = 4 ii. n = 1 to n = 3 iii. n = 6 to n = 4 iv. n = 7 to n = 5 v. n = 2 to n = 5 A. iii only B. i and ii only C. ii and iii only D. iii and iv only E. i, ii, and v 13. Which quantum numbers are needed to define the subshell? A. n only B. n and l C. l only D. m l only E. l and m l F. n, l, and m l 14. How many possible orbitals are there with n = 3 and m = 1? A. 1 B. 2 C. 3 D. 5 E. 9 15. Which is not a permissible set of quantum numbers? 11. Which of the following electron transitions in a hydrogen atom results in the greatest release of energy from the atom? A. n = 3 to n = 4 B. n = 1 to n = 3 C. n = 6 to n = 4 D. n = 7 to n = 5 E. n = 2 to n = 5 A. n = 2, l = 0, m l = 0 B. n = 3, l = 2, m l = 2 C. n = 2, l = 1, m l = 1 D. n = 3, l = 3, m l = 0 E. n = 4, l = 3, m l = 3 Follow-up question: Identify the subshell (if the quantum numbers identify a possible state). 12. If the Bohr model is used, what frequency of light would be required for ionization of hydrogen? A. 6.17 10 14 Hz B. 1.31 10 3 Hz C. 3.29 10 15 Hz D. 4.31 10 10 Hz E. None of the above is within 5% of the correct answer 16. For electron distributions, which of the following statements is/are true? 1. d orbitals have a spherical shape. 2. p orbitals have a high electron density at the nucleus. 3. s orbitals have no electron density at the nucleus. A. 1 and 2 B. 2 only C. 2 and 3 D. 3 only E. None of the statements is true Week 2 CHEM 110 -Fall 2013 32
17. Which of the following represents an orbital in which a 3d electron could be found? A. 1 only B. 2 only C. 4 only D. 1 and 5 E. 2 and 3 18. An electron is in the 4s orbital of the hydrogen atom. Which one of these statements is(are) true? i. This hydrogen atom atom is in the ground state. ii. A hydrogen atom with an electron in the 4d orbital will be degenerate with the electron in the state described above. iii. A hydrogen atom with an electron in the 3s orbital will be degenerate with the electron in the state described above. A. only i is true. B. only ii is true. C. only iii is true. D. ii and iii are true. E. None of these are true. Week 2 CHEM 110 -Fall 2013 33
Recitation Worksheet 1. What is the wavelength of light that has a frequency of 6.2 10 9 Hz and in what region of the electromagnetic spectrum can it be found? 2. Which one of the following photons is higher in energy than a green photon? A. Microwave photon B. ultra-violet photon C. Red photon D. Radio frequency photon 3. (A) What is the wavelength of one X-ray photon if the frequency is 1.00 10 19 s 1? (B) What is the energy of one X-ray photon of this frequency? (C) What is the energy of one mole of X-ray photons of the same wavelength? 4. There is a red emission line at 670nm in the line spectrum of Li. What is the energy difference between the energy levels involved in the electronic transition that produces this emission line? A. 2.97 10 19 J B. 6.70 10 7 J C. 4.48 10 14 J D. 9.89 10 28 J 5A. Which of the following electron transitions in a hydrogen atom will emit a photon, which absorb a photon? (How do you know?) A. n = 1 to n = 3 B. n = 4 to n = 3 C. n = 3 to n = 2 D. n = 3 to n = 1 E. n = 2 to n = 3 5B. Which of the above electron transitions in a hydrogen atom will result in emission of light with the longest wavelength? 6. Use the Bohr model and determine the wavelength of light that would ionize a hydrogen atom if the electron were in an excited state (n =3). (Hint: ionization is the removal of an electron; assume we are removing it from the n = 3 value) Week 2 CHEM 110 -Fall 2013 34
7A. An emission line the hydrogen atom has a wavelength of 93.8 nm. What region in the electromagnetic spectrum is this emission found? 7B. Determine the final value of n associated with this emission? (Hint: Consider E = h and the Rydberg equation, use this to find the value of n f.) 7C. Determine the initial value of n associated with this emission. (Hint: Will this value be higher or lower than n f and why is this the case? What equation will you use to determine this value; what values do you know?) 8. Consider the rules for assigning quantum numbers. Which is not a permissible set of quantum numbers? Identify the orbital (if possible) a) n = 2, l = 0, m l = 0 b) n = 3, l = 2, m l = 2 c) n = 2, l = 1, m l = 1 d) n = 3, l = 3, m l = 0 e) n = 4, l = 3, m l = 3 Hint: What quantum number(s) gives the electron shell? What quantum number number(s) indicate the subshell? Which quantum number(s) define the orbitals in a subshell? 9. Give the set of quantum numbers that describes each of the following orbitals assuming they are all in the third shell. A. B. C. D. ----------------------------------------------------------------------------------------------------------------------- Week 2 CHEM 110 -Fall 2013 35