# HW2_key - HW2_chapter 17 17-8 Q If Nw is the number of...

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HW2_chapter 17: 17-8: Q. If N w is the number of protons aligned with a magnetic field B z and N 0 is the number of protons opposed to the field, show that / 0 z B B k T w N e N Given that 7 1 1 26.7522 10 rad s  for a proton, calculate N 0 / N w as a function of temperature for a field strength of 5.0 T. At what temperature is N 0 = N w ? Interpret this result physically. A. The energy of the protons aligned with the magnetic field is 1 2 w z E B   , and the energy of the protons aligned against the magnetic field is 1 2 o z E B . Using Equation 17.10, we can write 1 1 exp exp 2 2 o z z z w B N B B B N k T For a field strength of 5.0 T, 34 7 1 1 23 1 (1.05459 10 )(26.7522 10 )(5.0 ) 0.010 exp exp (1.38066 10 ) o w N J s rad s N J T T   Let N 0 = N w , then 0.010 1 exp o w N N T , 0.010 0 T And T is undefined. Therefore, we can never attain the condition N 0 = N w . ( See section 15-3 for a similar problem, where we find that the population of the ground state is always greater than the population of the excited state in a two-level system.)

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