an unknown element crystallizes in a face-centered cubic unit cell. with an edge length of 392.4 pm. The solid has a density of 21.09 g/cm^3. what is atomic weight of solid?
so what i did was :
FC cubic uit --> 4 atoms
edge length--> l = 2*root2*r = 392.4 pm = 392.4 * 10^-8 cm.
d= 21.09 g/cm^3
d= m/l^3
m= l^3 * d
m= 8.2757*10^-5 g
1amu = 1.66054 * 10^-24 g
atomic weight = 4.98 * 10^19 amu.
and that is not the correct answer at all. where am i going wrong? please help :/
the options are :
a) 6.9 amu
b) 241.7 amu
c)74.4 amu
d) 191.8 amu
ryeng i suppose?
this is a very easy question
392.4*10-10= x cm
xcm^3= ycm^3
ycm^3* 21.09= mass in grams
since face centered unit cell has 4 atoms
mass/4, then use the product of that to divide by 1.66*10^-24 = amu
your result should be 191.84 amu
One place you erred is in the volume. You have a given to you (the edge length) so volume = a^3.
I agree with Tom's answer although I don't follow all of the work. My answer is 191.77 which rounds to 191.8 and that is one of the answers.
To solve this problem, you need to calculate the number of atoms in the unit cell and use the density to find the mass of the solid.
First, let's calculate the number of atoms in the face-centered cubic (FCC) unit cell. In an FCC unit cell, there are atoms located at each corner and one additional atom in the center of each face. So, a total of 4 atoms.
Next, you correctly calculated the edge length of the unit cell (l) as 392.4 pm, which is equal to 392.4 * 10^-8 cm. This is the length of one side of the cube.
Now, let's calculate the volume of the unit cell. Since it is a cube, the volume is equal to the length cubed (l^3).
Volume of unit cell = (392.4 * 10^-8 cm)^3
Now, use the density (d) to find the mass (m) of the solid:
d = m / V
m = d * V
Substituting the values:
m = 21.09 g/cm^3 * (392.4 * 10^-8 cm)^3
Calculate this mass to find the mass of the solid in grams.
Next, convert the mass from grams to atomic mass units (amu). You correctly used the conversion factor 1 amu = 1.66054 * 10^-24 g.
Finally, divide the mass in grams by the conversion factor to get the atomic weight of the solid in amu.
Check your calculations again with these steps, and you should be able to find the correct answer from the given options.