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Unformatted text preview: Astronomy C10 / L&S C70U: Fall 2010 Homework #2 Solutions Maximum points possible = 50 1. Absorption of Photons by Atoms (11 points total). (a) (2 points.) Which transition has the same energy as #1 #2 ? Jumping from state #1 to #2 is a jump of 5 of our energy units. There are two other such jumps. One is from state #2 to #5, the other is from state #5 to #7. [Graders: Either one OK for full credit.] (b) (3 points.) What is the ratio of energies of the photons emitted by a pair of downward jumps? Jumping from state #6 #4 is a change of (13 9) = 4 units. Jumping from #4 #3 is a change of (9 7) = 2 units. The ratio of energies is thus 2:1. [Graders: 1/2 is also valid if the student flips the ratio.] (c) (3 points.) Can the photon emitted by 3 2 be absorbed by an atom with electron in state 4? The jump from #3 #2 emits a photon with (7 5) = 2 energy units. Looking at the energy levels surrounding state #4, we see that jumping up to state #5 would take (10 9) = 1 unit, and a jump to state #6 would require (13 9) = 4 units. Absorption can only occur when the incoming photon has exactly the same energy that one of the electrons possible energy level jumps requires. No par tial absorption is possible. The emitted photon with 2 energy units is thus the wrong size for the #4 #5 jump and is too weak to be considered for any of the greater leaps. This photon will NOT be absorbed. (d) (3 points.) If the jump from state #2 #3 requires a photon with wavelength 5000 A, what is the wavelength needed for the #2 #4 jump? The energy associated with the jump from #2 #3 is (7 5) = 2 units. The jump from #2 #4 is (9 5) = 4 units. Thus, the larger jump will require (4 / 2) = 2 times the energy. The energy of a photon is directly proportional to its frequency. ( E = h, where h is Plancks constant Class Slide 25) However, the wavelength of a photon is inversely proportional to its frequency (recall wavelength times frequency = speed, so = c/ ). This means that energy is likewise inversely proportional to wavelength: E = hc/ . A photon with 2 times the energy of another thus has 1/2 the wavelength. In our case, the more energetic photon will then have a wavelength of 2500 A....
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 Fall '10
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