Tungsten crystallizes in a body-centered cubic unit cell with
an...

Question

Tungsten crystallizes in a body-centered cubic unit cell with 
an edge length of 317 pm. What is the length in picometers 
of a unit-cell diagonal that passes through the center atom?

Accepted Answer

Hello everyone today. We have the following problem. The crystal of chromium has a body centered cubic. Unit cell is edge length is 288 kilometers. If the unit cell diagonal passes through the center adam, what is the length of the diagonal in PICO meters? So first we have to determine our variables. So in the cube we have edges, A B and C. A. Is going to represent our edge length. B is going to represent our face diagonal length. N C. Is going to represent our body diagonal length. And according to the problem, we were given the edge line which is 288 PK meters. So our edge length was 288 m. We must then put together our formula for a body centered cubic unit cell, which is our B squared. So we're going to square the face diagonal and then we're gonna equal that to twice the squared of our edge length. Furthermore, if we break this formula down, we can see that our C square or the square of our body diagonal is equal to r squared of our edge plus the face diagonal squared. Since we established what B squared was equal to, we can go ahead and put that into our equation. So we'll have C squared is equal to a squared plus two A squared. This gives us a total of C squared is equal to three A squared to simplify and to isolate our C or our body diagonal. We square both sides. So we get to see is equal to three A or the Square Root of three A. Then we simply have to plug in our value for what A is. So he said A was 288 PK meters. So that's the square root of three times 288 PK meters. And this gives us a value When we simplify of 499 PK m as our final answer. And with that we've answered the question overall. I hope this helped. And until next time.

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