Vacancy Fraction Calculation for Copper at Melting Temperature

To calculate the fraction of atom sites that are vacant in copper at its melting temperature, we can use the equation for the vacancy concentration:

[

C_v = N cdot e^{-E_v/(kT)}

]

where:

– ( C_v ) is the vacancy concentration,

– ( N ) is the total number of atomic sites (not needed for fraction calculation),

– ( E_v ) is the vacancy formation energy (in eV),

– ( k ) is Boltzmann’s constant (8.617 x (10^{-5}) eV/K),

– ( T ) is the temperature in Kelvin.

Given:

– ( E_v = 0.90 ) eV,

– ( T = 1357 ) K.

First, calculate ( kT ):

[

kT = (8.617 times 10^{-5} , text{eV/K}) times 1357 , K approx 0.116 , text{eV}

]

Now, plug in ( E_v ) and ( kT ):

[

C_v = e^{-0.90 , text{eV} / 0.116 , text{eV}} approx e^{-7.7586} approx 0.0005

]

So, the fraction of atom sites that are vacant for copper at its melting temperature is approximately **0