Chapter 40: Q26E (page 1219)
In Problems 13-32 use variation of parameters to solve the given nonhomogeneous system.
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How many electron states are in these sub-shells: (a) n = 4,l = 3 ; (b) n = 3, l = 1 ; (c) n = 4, l = 1 ; (d) n = 2, l = 0 ?
If orbital angular momentum is measured along, say, a z-axis to obtain a value for , show thatrole="math" localid="1661497092782" is the most that can be said about the other two components of the orbital angular momentum.
A hydrogen atom in its ground state actually has two possible, closely spaced energy levels because the electron is in the magnetic field of the proton (the nucleus). Accordingly, energy is associated with the orientation of the electronโs magnetic moment relative to , and the electron is said to be either spin up (higher energy) or spin down (lower energy) in that field. If the electron is excited to the higher energy level, it can de-excite by spin-flipping and emitting a photon. The wavelength associated with that photon is 21 cm. (Such a process occurs extensively in the Milky Way galaxy, and reception of the 21 cm radiation by radio telescopes reveals where hydrogen gas lies between stars.) What is the effective magnitude of as experienced by the electron in the ground-state hydrogen atom?
A certain gas laser can emit light at wavelength 550 nm, which involves population inversion between ground state and an excited state. At room temperature, how many moles of neon are needed to put 10 atoms in that excited state by thermal agitation?
For the situation of Problem 23, what multiple of gives the energy of (a) the first excited state, (b) the second excited state, and (c) the third excited state of the system of eight electrons? (d) Construct an energy-level diagram for the lowest four energy levels of the system.
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