tivistic corrections to the hydrogen energy are of the same treatment of fine structure must include both effects. order as the spin-orbit correction. Therefore, a correct the Pauli Pri and Periodic momentum er that the = ev/2mr, y the elec- SECTION 9.8 (Magnetic Resonance Imaging ") 9.24 Just as the electron magnetic moment is given approximately by the Bohr magneton (9.17), the ni clear magnetic moment is conveniently expressed in terms of the nuclear magneton, e, you can bit of the this gives l calcula- used the you had uld have eh 10.1 Introduction (9.41) 2mp 10.2 The Independent-Particle Ap 10.3 The IPA Energy Levels 10.4 The Pauli Exclusion Principle 10.5 Fermions and Bosons; the O 10.6 Ground States of the First Fe 10.7 The Remaining Elements 10.8 The Perio dic Table 10.9 Excited States of Atoms where is the proton mass. (a) Find the value of тр in eV/T. Compare this with the Bohr magneton. (b) The proton's magnetic moment is found to be 2.7934N. (This common statement means that the two values of ±2.793 uN.) Find the energy-level separation for proton in a magnetic field B 1 T. re is an- ent used n's rest ) and Thomas ed here and somewhat ambiguous are hat our 9.25 Use the results of the previous problem to show that nificant for a proton in a B = 1-tesla field, the energy-level spitting corresponds to a frequency of 42.6 MH2. 9.26 According Problems for Chapter 10 L = 2h separa- These sections can be omitted wit nar- es of L, are mh, en eh AE mB 2me (9.16) As anticipated, the magnetic field changes the atom's energy by an amount that on the quantum number m. This is why m is often called the magnetic depends quantum number, and it explains the traditional choice of the letter m. ent Comparing (9.16) with (9.14) (and remembering that the quantum ber m is dimensionless), we see that the quantity in parentheses, (eh/2me), must have the dimensions of a magnetic moment. (You should check this directly; see Problem 9.14.) In atomic physics this quantity is a convenient unit for magnetic moments and is called the Bohr rgy num- o- om ed ct with the value magneton PB eh (9.17) 9.27 X 10 24 A m2 2me , we can rewrite (9.16) in the compact form In terms of uB (9.18) AE = mpBB Since m can have the 21 + 1 values 1,1-1, .., -1, we see that the 2/ + 1 dies of the original degenerate level now have energies that are equally