Question

Calculate the concentration of vacancies in in fcc silver at 250oC given that the activation energyfor vacancy creation in silver is 79.5 kJ/mol. The units for your answer should be vacancies/cm3.

Answer 1

Answer:

The concentration of vacancies in fcc silver is $6.6105\times 10^1^4 vacancies/cm^3$

Explanation:

Given is - silver (fcc lattice)

Temperature = 250°C = 523K

Activation energy for vacancy creation ,$Q_v$ =79.5 kJ/mol

Silver has a fcc crystal lattice structure with basis

Lattice parameter = 0.49nm = $4.09\times 10^-^8$m

Now , let us calculate number of silver atoms"(lattice points)per $cm^3$

 $N=\frac{4atoms/cell}{4.09\times10^-^8cm^3}$

     =$5.86\times10^2^2 Ag$ atoms/$cm^3$

Concentration of vacancies is given by the formula -

 $N_v =N_e_x_p\frac{-Q_V}{R.T_}$

here,

$N_v = concentration of vacancies$

$N= number of atoms$ $per$ $cm^3$

$Q_v=$ Activation energy for vacancy creation

T = Temperature

R = constant =$8.314 J K^-^1 mole^-^1$

Now , putting the given values in the formula -

$N_v= (5.85\times10^2^2atomscm^-^3)exp(\frac{-79.5KJ/mole}{8.314\timesJK^-^1mole^-^1})$

      =$6.6105\times10^1^4vacnacies/cm^3$

Hence , the answer is $6.6105\times10^1^4vacnacies/cm^3$