mp-Chapt-7-sol - Chapter 7 1. Problem Solutions A beam of...

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Inha University Department of Physics 1. A beam of electrons enters a uniform 1.20-T magnetic field. (a) Find the energy difference between electrons whose spins are parallel and antiparallel to the field. (b) Find the wavelength of the radiation that can cause the electrons whose spins are parallel to the field to flip so that their spins are antiparallel. (a) Using Equations (7.4) and (6.41), the energy difference is, Chapter 7 Problem Solutions eV 10 39 1 T 20 1 eV/T 10 79 5 2 2 2 4 5 - - × = × = = = . ) . )( . ( B B E B sz m m (b) The wavelength of the radiation that corresponds to this energy is Note that a more precise value of AB was needed in the intermediate calculation to avoid roundoff error. mm 93 8 eV 10 39 1 m eV 10 24 1 4 6 . . . = × × = = - - E hc l 3. Find the possible angles between the z axis and the direction of the spin angular-momentum vector S. For an electron, and so the possible angles axe given by , ) / ( , ) / ( h h 2 1 2 3 ± = = z s s o o 3 125 7 54 3 1 2 3 2 1 . , . arccos ) / ( ) / ( arccos = = ± h h sol sol
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Inha University Department of Physics 5. Protons and neutrons, like electrons, are spin-½ particles. The nuclei of ordinary helium atoms, , contain two protons and two neutrons each; the nuclei of another type of helium atom, , contain two protons and one neutron each. The properties of liquid and liquid are different because one type of helium atom obeys the exclusion principle but the other does not. Which is which, and why? He 4 2 He 4 2 He 3 2 He 3 2 atoms contain even numbers of spin-½ particles, which pair off to give zero or integral spins for the atoms. Such atoms do not obey the exclusion principle. atoms contain odd numbers of spin-½ particles, and so have net spins of and they obey the exclusion principle. He 4 2 He 3 2 , , 2 5 2 3 2 1 or 7. In what way does the electron structure of an alkali metal atom differ from that of a halogen atom? From that of an inert gas atom? sol An alkali metal atom has one electron outside closed inner shells: A halogen atom lacks one electron of having a closed outer shell: An inert gas atom has a closed outer shell. sol
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Inha University Department of Physics 9. How many electrons can occupy an f subshell? sol For f subshell, with l = 3, the possible values of m l are ±3, ±2, 1 or 0, for a total of 2 l +1=7 values of m l . Each state can have two electrons of opposite spins, for a total of 14 electrons. 11. If atoms could contain electrons with principal quantum numbers up to and including n = 6, how many elements would there be? sol
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mp-Chapt-7-sol - Chapter 7 1. Problem Solutions A beam of...

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