A hydrogen atom in its ground state actually has two

Chapter , Problem 18

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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, an energy is associated with the orientation of the electrons 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?