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.
1. 1.18 x 10^(-5)
2. 8.80 x 10^(-4)
3. 4.05 x 10^(-7)
4. 2.30 x 10^(-3)
Question & Answer
Calculation of Vacant Atom Sites in Lead at Melting Temperature
1 Answer
Verified archiveTo calculate the fraction of vacant atomic sites (f_vac) in lead at its melting temperature, we can use the equation:
[ f_{vac} = e^{-frac{E_v}{kT}} ]
Where:
– ( E_v ) is the energy for vacancy formation (0.55 eV),
– ( k ) is Boltzmann’s constant (8.617 x 10^(-5) eV/K),
– ( T ) is the temperature in Kelvin (600 K).
1. Calculate ( frac{E_v}{kT} ):
[ frac{E_v}{kT} = frac{0.55 text{ eV}}{(8.617 x 10^{-5} text{ eV/K}) times 600 text{ K}} ]
[ = frac{0.55}{0.051702} approx 10.65 ]
2. Now calculate ( f_{vac} ):
[ f_{vac} = e^{-10.65} approx 2.25 times 10^{-5} ]
Approximating this, the correct fraction of vacant atomic sites can be found closest to:
Answer: 1.18 x 10^(-5)
Thus, the answer is 1.18 x 10^(-5). If you have more questions or need further clarification, feel free to ask!