hree spectral lines, however the angular momenta involved.) netic lec- ) as tan- SECTION 9.5 (Spin Magnetic Moments) 9.18 The electron's total magnetic moment is given by (9.25). (a) What are the possible values of for an electron with/ = 0? (b) Compare these with the values of u for a hypothe tical spinless electron with / 1. a p e to )? SECTION 9.6 (The Anomalous Zeeman Effect) 9.19 Consider a hydrogen atom in its ground level, placed in a magnetic field of 0.7 T along the z axis. (a) What is the energy difference between the spin-up and spin-down states? (b) An experimenter wants to excite the atom from the lower to the upper state by sending in photons of the appropriate energy. What energy is this? What is the wavelength? What kind of radiation is this? (Visible? UV? etc.) nd e. e e Consider a hydrogen atom in the 3d state with itc eneroy 9.20 08 Chapter 9 Electron Spin and would be completely unaffected by a magnetic field. In fact, of course, the 0, there is a magnetic momen electron does have spin and, even though / (9.26 u spin me When a magnetic field B (in the z direction) is switched on, the energy changes *otos 1Lace by an amount s,B 6F AE =.B me there is no external magnetic field, this intemal field of the energy levels and, hence, of the atomic spectru the internal magnetic field are called fine structure scribe briefly the fine structure of hydrogen,many o found to be doublets consisting of two closcly spac Since the possible values of S, are it follows that Tet us consider the states of a bydrogen atom eh B = tpBB 2me (927) (given by quantum number n) and definite non tum (given by quantum number 1). We can und these states from the following semiclassical areL electron, the proton orbits around the electrona the electron finds itself in the magnetic field an orbiting positive charge. This field is propor of the proton (as seen in the electron's rest tional to the orbital angular momentum L of AE = ± If the electron has spin up, its energy is raised by uBB; if it has spin down its energy is lowered by the same amount. The resulting separation of the tun levels is therefore (9.28 (separation of levels) 24BB Notice that this separation is twice the value (9.19) predicted for the normal Zeeman effect; this is because the spin gyromagnetic ratio is twice the or ton's rest frame. Therefore, the electron sees a BoL bital ratio. We conclude that any / = 0 level in hydrogen should be split into two neighboring levels by a magnetic field. This splitting is sketched in Fig. 9.5 As can be seen in Fig. 9.6, the direction of B That thac

hree spectral lines, however the angular momenta involved.) netic lec- ) as tan- SECTION 9.5 (Spin Magnetic Moments) 9.18 The electron's total magnetic moment is given by (9.25). (a) What are the possible values of for an electron with/ = 0? (b) Compare these with the values of u for a hypothe tical spinless electron with / 1. a p e to )? SECTION 9.6 (The Anomalous Zeeman Effect) 9.19 Consider a hydrogen atom in its ground level, placed in a magnetic field of 0.7 T along the z axis. (a) What is the energy difference between the spin-up and spin-down states? (b) An experimenter wants to excite the atom from the lower to the upper state by sending in photons of the appropriate energy. What energy is this? What is the wavelength? What kind of radiation is this? (Visible? UV? etc.) nd e. e e Consider a hydrogen atom in the 3d state with itc eneroy 9.20 08 Chapter 9 Electron Spin and would be completely unaffected by a magnetic field. In fact, of course, the 0, there is a magnetic momen electron does have spin and, even though / (9.26 u spin me When a magnetic field B (in the z direction) is switched on, the energy changes *otos 1Lace by an amount s,B 6F AE =.B me there is no external magnetic field, this intemal field of the energy levels and, hence, of the atomic spectru the internal magnetic field are called fine structure scribe briefly the fine structure of hydrogen,many o found to be doublets consisting of two closcly spac Since the possible values of S, are it follows that Tet us consider the states of a bydrogen atom eh B = tpBB 2me (927) (given by quantum number n) and definite non tum (given by quantum number 1). We can und these states from the following semiclassical areL electron, the proton orbits around the electrona the electron finds itself in the magnetic field an orbiting positive charge. This field is propor of the proton (as seen in the electron's rest tional to the orbital angular momentum L of AE = ± If the electron has spin up, its energy is raised by uBB; if it has spin down its energy is lowered by the same amount. The resulting separation of the tun levels is therefore (9.28 (separation of levels) 24BB Notice that this separation is twice the value (9.19) predicted for the normal Zeeman effect; this is because the spin gyromagnetic ratio is twice the or ton's rest frame. Therefore, the electron sees a BoL bital ratio. We conclude that any / = 0 level in hydrogen should be split into two neighboring levels by a magnetic field. This splitting is sketched in Fig. 9.5 As can be seen in Fig. 9.6, the direction of B That thac