1. The diagram above shows three energy levels of a hypothetical atom. The lowest available energy level is E1 = -5.0 eV. E, = -5.0CV a) Draw arrows on the above diagram showing all possible photon emissions for electrons that begin in the -2.2 ev state. b) What wavelength(s) of visible light can electrons emit that begin in the -2.2 e V state?" c) Make a graph of the maximum kinetic energy AEmax of ejected electrons as a function of the wavelength ^ of the incident light for the range of wavelengths indicated. Label the vertical axis with an appropriate scale and units. d) What is the stopping potential for electrons ejected from this surface by 100 nm radiation? 2. Suppose that an electron within a hydrogen atom moves from the fourth energy level to the second energy level. What is the wavelength of the photon emitted during this process? 3. The figure above shows the energy-level diagram for a hypothetical simple atom. The wavelength of the radiation emitted when an electron undergoes B transition B is 400 nm, and for transition C it is 700 nm. a) Calculate the wavelength of the radiation emitted when an electron Ic makes transition A. The photon emitted during transition B is then incident on a metal surface of work function 2.46 eV. b) Calculate the maximum kinetic energy of the electron ejected from the metal by the photon. c) Calculate the de Broglie wavelength of the ejected electron. 4. The diagram shows the lowest four discrete energy levels of an atom. An electron in the n=4 state makes a transition to the n=2 state, emitting a 1=3 6.04 ev photon of wavelength 121.9 nm. -13.6 ev a) Calculate the energy level of the n=4 state. b) Calculate the momentum of the photon. -544 ev The photon is then incident on a silver surface, and the surface emits an electron with maximum possible kinetic energy. The work function of silver is 4.7 eV. c) Calculate the kinetic energy, in ev, of the emitted electron. d) Determine the stopping potential for the emitted electron. 5. An atom's ground state is -8.0 eV. The absorption spectrum for the atom has lines at 249 nm and 829 nm. Each line corresponds a transition from ground state to an excited state. a) Draw an energy level diagram. b) If the atom makes a transition from its higher excited state to its lower excited state a photon is given off. Calculate the frequency and wavelength of this photon. c) A photon of wavelength 124 nm imparts of its energy to an electron when the atom is in ground state. The atom is ionized. What is the kinetic energy of the result free electron?5. An atom's ground state is -8.0 eV. The absorption spectrum for the atom has lines at 249 nm and 829 nm. Each line corresponds a transition from ground state to an excited state. a) Draw an energy level diagram. b) If the atom makes a transition from its higher excited state to its lower excited state a photon is given off. Calculate the frequency and wavelength of this photon. c) A photon of wavelength 124 nm imparts of its energy to an electron when the atom is in ground state. The atom is ionized. What is the kinetic energy of the result free electron? d) What is the speed of the free electron? (electron mass is 9.1 1x10 31 kg). 6. The energy level diagram for a hydrogen atom is shown. n = = 0.00 ev a) Does the diagram to the right represent emissions or absorptions? How do n = 5 -0.544 eV you know? n=4 0.850 ev b) An electron jumps from n = 4 to n = 1. What is the energy in ev of the n= 3 -1.51 ev associated photon? Is the photon emitted or is it absorbed by the hydrogen atom? Which series is this photon associated with? What is its frequency? c) A photon having an energy of 12.09 ev strikes a hydrogen atom. Can it be n =2 -3.40 ev absorbed by the atom? If so, describe the electron jump that will occur. d) An electron jumps from n = 4 to n = 2. What will be the energy of the associated photon? Will this photon be emitted, or will it be absorbed? () What is the wavelength of the previous photon in nm? What is its frequency? -13.6 ev 7. The electron energy levels above are for an electron confined to a certain very small one-dimensional region of space. The energy E,, of the levels, where n = 1, 2, 3, . . ., is given by En = n'E1. Express all algebraic answers in terms of E, and fundamental constants. a) Label the three excited energy levels with the values for their energies in terms of El , the energy of the ground state b) Calculate the smallest frequency of light that can be absorbed by an electron in this system when it is in the ground state, n = 1. c) If an electron is raised into the second excited state, draw all the possible transitions that the electron can make in returning to the ground state