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PHY 102 Lab #25: Hydrogen Atom Model According to Bohr's theory, the energy of the stable orbits of the hydrogen atom are given by In 1913, Neils Bohr postulated that the electron in a hydrogen atom could exist in one of several stable states or En = -21.8 x 10 ' J orbits in which it would not emit electromagnetic radiation. Light c adiation. Light could be emitted or absorbed by the atom only if the electron jumped from one of these orbits to another. Thus, the energy levels of the atom were where n is the quantum number of that orbit. quantized. Now, let's draw an energy level diagram for hydrogen in the box provided. Start with a horizontal line to A few years later, Louis DeBroglie hypothesized that if electromagnetic waves have particle-like properties like represent the ground state (n = 1) near the bottom. Calculate the energy of this state; show your work. momentum, then perhaps particles have wave-like properties. In analogy with the equation for the momentum of a photon, p = h/2, the wavelength of such a particle would be given by B1 = 2 = h/p= h/mv. Let us see how this idea helps explain the quantum levels in a hydrogen atom. Label the line representing this ground state in your diagram with its quantum Energy Level Diagram number and energy. According to Bohr's theory of the hydrogen atom, the allowed electron orbits have radii which are given by the formula Calculate the energy of the first excited state, n = 2. In =(0.53 x 10 m) n E2 = where n is the quantum number of the orbit; n = 1, 2, 3... = 10" J draw this level on your diagram according to Calculate the radii of the first three orbits of hydrogen. Show your work. Using a scale of 1 cm = 10" cantun the specified scale and label it with its quantum number and energy in the box provided. 1 = I Continue with n = 3, 4, and 5. Calculate the energies and draw the lines. E3= EA Assuming that these orbits are circular, calculate the circumference, on, of each of the first three orbits. Recall that c = 2xtr. Show your work. CL = Es = C2 = What happens to the spacing between the levels as the energy increases? Using a scale of 10 cm = 1.0 x 10-10 m, draw on a piece of paper a straight line whose length represents circumference c1. With this line as an axis, sketch a sine wave whose wavelength is equal to this distance. The If an electron at n = 3 were to go to level n = 2, how much energy would it lose? Why? amplitude should be about 1.0 cm. Label this wave n=1. Repeat for the n =2 orbit, but this time draw a wave whose length is half of the circumference, that is, two full wave fit into the length of the line. th of the line. Then repeat for n=3 with three waves. Cut out these strips of paper and tape If a photon were emitted in this process, what would its frequency be? Show how you got this? the ends together to form rings so that the ends of the sine waves match up. If the ends of the wave match, then a standing wave of that wavelength can oscillate around a circle of that circumference. What would happen to a wave whose wavelength did not match the circumference? What would its wavelength be? Show your work. Convert this to nm using 10" m = 1 nm Now, arrange the rings with n = 1 at the center and n = 2 and n = 3 around it. Attach this scale model of the hydrogen atom's first three orbits below. Would it be visible? How can you tell? What color would it be? How do you know? Check the spectrum chart for hydrogen and identify this line. What was its measured wavelength? (it will be slightly different from yours due to rounding) Repeat steps using a transition from energy level n = 4 to n = 2. Show your work. Energy Energy Level Diagram Frequency = Wavelength = Visible? Color = If a hydrogen atom in its ground state absorbed a photon and jumped to the first excited state, what would the wavelength of that photon be? Explain. In what part of the spectrum would this light be