Problem 12: A hydrogen atom in an excited state has an energy, E = -0.85 eV. It makes a transition to a different state where its energy is E = -3.4 eV. a) What are the quantum numbers of the two states? b) What is the wavelength of the emitted photon? As part of your answer, you must include a diagram showing the transition on an energy level diagram for hydrogen. Problem 13: A spaceship from another galaxy passes over the solar system directly above and parallel to a radial line from the Sun to the Earth. We, on Earth, measure the Earth-Sun distance to be 1.50 x 10¹¹ m and measure the speed of the spaceship to be 0.8c. a) What does a scientist in the spaceship measure the Earth-Sun distance to be? b) How long does the trip take according to a clock in the spaceship? Problem 14: The starships of the Solar Federation are marked with the symbol of the federation, a circle, while starships of the Denebian Empire are marked with the empire's symbol, an ellipse whose major axis is 1.40 times longer than its minor axis (a = 1.40 b) as shown in the figure. How fast, relative to an observer, does an empire ship have to travel for its marking to be confused with the marking of a federation ship? K Federation Empire Problem 15: An 18-mm wide diffraction grating has rulings of 880 lines per mm. Monochromatic light of 590 nm wavelength is incident normally on the grating. Determine the largest angle, measured from the central bright spot, at which an intensity maximum is formed.