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## Homework Statement

The number of vacancies in a metal increases by a factor of six when the

temperature is increased from 800K to 1000K. Calculate the energy for vacancy

formation assuming that the density of the metal remains the same over this

temperature range.

## Homework Equations

N

_{v}= N exp ( -Q

_{v}/ kT)

where N

_{v}= equilibrium number of vacancies

N = total no. of atomic sites

N is dependent on density etc, there is a formula but i dont believe it is needed for this problem.

-Q

_{v}= energy required for vacancy formation ( in eV)

k = Boltzmann’s constant (1.38 x 10

^{-23}JK

^{-1}or 8.62 x 10-5eVK

^{-1})

T = temperature (in kelvin)

## The Attempt at a Solution

What I attempted to do was a simultaneous equation, taking the fact that N

_{v}at 1000K is 6x more than N

_{v}at 800k

N

_{v}= N exp ( -Q

_{v}/ 8.62 x 10

^{-5}eVK

^{-1}x 800)

and

6N

_{v}= N exp ( -Q

_{v}/ 8.62 x 10

^{-5}eVK

^{-1}x 1000)

so hence i thought

6 (N exp ( -Q

_{v}/ 8.62 x 10

^{-5}eVK

^{-1}x 800)) = N exp ( -Q

_{v}/ 8.62 x 10-5eVK

^{-1}x 1000)

From here things got a bit crazy, I still don't really understand what exp means (I used wolfram to try and solve and it told me exp just ment e^(whatever is infront of exp). Not sure if I'm doing things right.. but a few more steps and I just kept getting -Q

_{v}as zero. Help would be great thanks alot.

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