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3. Particle in a Box (a) Consider an electron confined to a 1-dimensional box of length L= 1.35 Å = 1.35 ×10–10which is the length of a C=C double bond. This is a model for an electron in the higher molecular orbitals of the ethylene (H2C=CH2) molecule. What are the allowed de Broglie wavelengths for the ground (state 1) and first excited state (state 2)? m, (b) What is the separation in energy between the ground and first excited states in this model? (c) What wavelength of light can be used to excite the system from the ground state to the first excited state? Wavelength = _____________________ m Part and max points (a) 5 (b) 5 (c) 5 Total (15) Your score
Page 5 of 10 4. The Hydrogen Atom (a) The Lyman series of lines in the emission spectrum of the hydrogen atom occurs in the vacuum ultraviolet region of the electromagnetic spectrum. These lines involve transitions from higher-energy states (principal quantum number n> 1) to the n= 1 ground state. Compute the wavelength of the first transition in this series, namely the n= 2 to n= 1 transition. Wavelength = _________________________________ m (b) Draw a plot of the radial part of the wave function for the 1sorbital of the hydrogen atom. (c) Draw a plot of the 2pxorbital in the xyplane. Part and max points (a) 5 (b) 5 (c) 5 Total (15) Your score