Calculate the fraction of atom sites that are vacant for lead at its melting temperature of 327°C (600 K). Assume an energy for vacancy formation of 0.55 eV/atom.
N = (Na)(p)/A
Nv = N exp (-Q/kT)
Na = avogadro's number
p = density
A = atomic weight
Nv = number of vacancies
N = number of atomic sites / number of atoms
Q = the energy for vacancy formation
k = Boltzmann constant (can be 8.62E-5 eV/K or 1.38E-23 J/(atom)(K) )
T = temperature in Kelvin
The Attempt at a Solution
I have a sample problem done for me in the textbook. Doing the exact equation that's in the book, with all of the variables given to me, I get an incorrect answer. This happens no matter what calculator I use. Intermittent rounding gives a very wrong answer. Plugging it all in at once gives a consistent answer of 0.
Using lead A = 207.2, the eV/K boltzmann's constant, and all the other information, I get either 0 or 7.46E24 vacancies. The options are: 1.52E-11, 5.84E-8, 4.03E-6, and 16.66 .