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CHEM 109 Introduction to Chemistry Fall 2010 The Behavior of Electrons in Atoms In this short exercise we will examine how electrons behave within an atom. We will do this by looking at the energies of photons emitted when an excited atom relaxes. These excited atoms can be generated by placing the atom in the very large electric field within a gas discharge tube (think neon light) or in the heat of a Bunsen burner flame. Photons are particles of light that carry energy. Spectrum of the Hydrogen Atom In the laboratory we have observed the spectrum of photons emitted by excited Hydrogen atoms. Hydrogen is particularly important because 1H is the simplest atom possible. It contains a single proton in the nucleus and a single electron in the remaining space of the atom. This atom produced three spectral lines; Red, Blue, and Violet. These lines are only a part of the complete spectrum of Hydrogen. Other spectral lines occur in the Ultraviolet and Infrared regions of the electromagnetic spectrum. However, our eyes are not capable of registering these photons and so we do not see them. A more complete spectrum for Hydrogen is attached. We now wish to convert the energies of the emitted spectral photons into atomic energy levels for the excited atom. We do this by recognizing that photons are emitted when the atom transitions from a high energy state (excited) to a low energy state. This can be represented diagrammatically as below: Questions: 1. What is the minimum number of quantum states required to explain the three spectral lines observed in the laboratory? Diagram these and identify the transitions responsible for producing each spectral line. Your diagram should be to scale. (You calculated the needed photon energies in the last laboratory exercise.) What assumption do you have to make in order to construct this diagram? 2. Our visible spectral lines are part of a grouping of spectral lines called the Balmer Lines. What do you notice is happening to the lines in this series as the energy of the emitted photons increases? What implications does this have for the energies of Hydrogen’s quantum states? Indicate this on your energy diagram? 3. What additional piece of information do you need in order to confirm the order of your quantum states is correct? (Hint: Look to the complete Hydrogen spectrum for the spectral line that will provide the needed information.) Consult your Teaching Assistant for the information you need. 4. What are the photon energies associated with the first two spectral lines of the Lyman Series that occurs in the Ultraviolet region of the electromagnetic spectrum? How will your energy diagram need to be modified in order to account for the quantum states associated with these spectral lines? Re-draw your energy diagram to account for the new quantum states. The lowest energy state possible is referred to as the Ground State. Label this in your diagram. Each quantum state is labeled with a quantum number; starting with the ground state (n=1). The other states are labeled consecutively with integer increases. Label each state in your diagram with its quantum number. What is the largest quantum number possible? Interactions within the Hydrogen Atom 5. What is the nature of the interaction between Hydrogen’s nucleus and its electron? 6. Will this interaction be stronger or weaker as the electron moves away from the nucleus? 7. Bohr built one of the first successful models of the Hydrogen atom. In this model, the electron orbits the nucleus with a given velocity. Which are energetically more favorable, orbits close to the nucleus or those further from the nucleus? Explain your choice. 8. Why will the electron’s velocity not cause it to fly out of the atom? 9. What is the minimum number of orbits required to account for the three visible spectral lines of the Balmer series? Correlate each orbit with a quantum state in your energy diagram by labeling the orbits with an appropriate quantum number. 10. By balancing the Centrifugal and Electrical forces within the atom, Bohr was able to develop an expression for the radius of the electron’s orbit based on the orbit’s quantum number (n). radius = 0.052917 x n2 Sketch to scale the orbits associated with the first 4 quantum states. 11. What “orbit” is associated with the “largest” quantum number? Hydrogen-Like Atoms The following atoms are called Hydrogen-like atoms: He+, Li2+, Be3+, etc. 12. How are these atoms Hydrogen-like? What is the next atom in this series? 13. How will the orbits of the electrons in these atoms differ from the corresponding orbits in the Hydrogen atom? Explain your reasoning. 14. Bohr’s model for the Hydrogen atom can be modified to include these Hydrogen-like atoms by including the charge on the nucleus (Z): radius = 0.052917 x Z x n2 Sketch to scale the orbits associated with the first 4 quantum states for He+. 14. What will happen to the spectral lines associated with these states when compared to similar states in the Hydrogen atom? Explain your reasoning. Helium Atom Now consider the next more complex atom; that of 4He. 15. What additional interactions occur within this atoms? Appendix - Complete Emission Spectrum of Hydrogen