4, 3. Excited Ground state 1(ground state) state 4. 4.85E-19 J 4.42E-19 J 3.98E-19 J 3. 1. 3.03E-19 J 2. 1. 1 (ground state) Energy Energy paquosqe emitted 2) [30] Energy Levels Above is a schematic of a Hydrogen atom with its first 5 energy levels. On the right is the energy emitted from the transitions (lines pointing down on the diagram). Using the knowledge that energy and wavelength are hc, connected ( E =) you will figure out the wavelength for each of these %3D transitions. %3D E. h = Planck constant = 6.63E-34 J*s c = speed of light = 3E8 m/s 2 = wavelength in meters E = energy in Joules (J) %3D hc %3D E will be in meters! Divide by 10-9 for nm If you need help converting this to a color easier, try this website once you get the wavelength in nm: https://academo.org/demos/wavelength-to- colour-relationship/ For the following give the wavelengths in nanometers (nm) and no decimal points needed. The above equation is in meters! A nanometer is 10° meters. ALL ANSWERS ARE IN VISUAL, so they should all be between 400- 700 nm range. This is important to be able to do on your calculator, so hopefully knowing the range helps double check your answer! a) The electron can absorb energy to go to any of the higher energy levels. If it gets absorbed to the 4th excited state (the top line labeled 5), what wavelength does the atom emit if it goes from this state (5) back to the ground state (1)? What color is this? tariw (1)eti2 bruong ard of S) 9a betioxe orh mol yltes (b froloo tadw bns rignslovsw Sagan mea We are matle of star b) The electron can go to any state depending on the energy absorbed. What wavelength does the atom emit if it goes from the 3rd excited state (4) to the ground state (1)? What color is this? about finding planets an poasibly e an young sten?

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Question 14 a) A narrow beam of white light is passed through a clear glass vessel containing cool hydrogen gas at a low pressure. A prism is used to disperse the light leaving the vessel. This results in a white light spectrum, crossed by a series of dark lines. Explain the origin of these dark lines and name the type of spectrum that is produced. b) Some of the atomic energy levels of hydrogen are shown in the diagram below. i. ii. iii. Energy/eV 0 -0.85 -1.51 -3.39 -13.58 n = 4 n = 3 n = 2 n = 1 Determine the ionization energy of hydrogen and express this in joules. Determine the wavelength of the light emitted when an electron falls from the n = 3 level to the n = 1 energy level. A photon of energy 10.19 eV is in collision with a hydrogen atom. What would happen to this photon?

Question B3 One of the possible states of the electron in the Hydrogen atom is given by 1 r (r, 0, 0) = e -r/(200) sin eo, 3/2 where a is the Bohr radius. For this wavefunction, answer the following questions: a) Using the operator for the z-component of angular momentum ₁₂ = -ihǝ/ǝo, determine the value of the quantum number m₁. [4 marks] b) Using the total angular momentum operator, given below, determine the value of the quan- tum number 1. a β = -h² 1 მ sinᎾ [sin € 30 (sin 600) + 1098] sin2 c) d) [8 marks] Explain how you could have identified / and my by direct inspection of the wavefunction, and use the direct inspection method to identify the value of the quantum number n. The operator for the y-component of angular momentum is given by Ly = ih ih (-cos - მ a +cot sin o მი (i) Calculate, and show that it is not a function of o. (ii) Show that the expectation value of I, vanishes, i.e. (L) = 0. [Hint: the volume element in this case is given by dV = 2 sin 0 dr de do.] [6 marks]…