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Calculation of Vacant Atom Sites in Lead at Melting Temperature

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)




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1 Answer

  1. To 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!

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