Calculate the surface energy of the (100) plane of niobium. The heat of atomization is 745 kJ/mol.
Express your answer in J/cm2.
The enthalpy of atomization of nobium is 745 KJ/mole.
The energy per atom is = 745000/Avogadro Number = 1.2371305e-18 J/atom
In a BCC structure each atom has 8 neighbors. Then
The energy per bond is = 1.2371305e-18 / 8 = 1.5464132e-19 J/bond
Now in a (100) plane the atoms density per unit area is = 4 (1/4) / a * a = 1/a2
For Nobium a = (2*92.91 / 8.57 * Avogadro number)^(1/3) = 3.30210056e-8 cm
Then the atoms density is 9.1710574e+14 atoms/cm2
Finally:The broken bonds are 4 per UC then (consider half for each surface)
Surface energy (100) =1/2 * 4 * Atoms density * Bond Energy = 0.00028364488 J/cm2
incorrect because bond energy is off by a factor of two because at 8 per atom you counted bonds twice.
and this is an mit 3.091 cheat. shame on you.
ivo said 6.23 e -3 works. anyone try?
yeb..wrong again
6.23 e -3 is wrong..
this is an exam question
cheater alert
To calculate the surface energy of the (100) plane of niobium, we can use the equation:
Surface Energy = Heat of Atomization / Surface Area
1. First, we need to determine the surface area of the (100) plane of niobium. The (100) plane is a square, so we need to find the area of one side.
2. The next step is to convert the heat of atomization from kJ/mol to J/atom. To do this, we divide the heat of atomization by Avogadro's number, which is approximately 6.022 x 10^23 mol^-1.
3. Finally, we convert the surface area to cm^2 and divide the heat of atomization by the surface area to find the surface energy in J/cm^2.
Let's calculate it step by step:
Step 1: Determine the surface area of the (100) plane of niobium.
The (100) plane of a cube has four equivalent sides since it is a square. The surface area of one side is given by:
Surface Area = Side Length * Side Length
To find the side length, we need to know the lattice constant (the length of the cube's edge) of niobium. The lattice constant for niobium is 3.3 Å (angstroms).
Converting Å to cm:
1 Å = 1 x 10^-8 cm
Side Length = 3.3 Å * (1 x 10^-8 cm / 1 Å) = 3.3 x 10^-8 cm
Step 2: Convert the heat of atomization to J/atom.
Heat of Atomization = 745 kJ/mol
Conversion factor: 1 kJ/mol = 1000 J/1 mol
Heat of Atomization (J/atom) = 745 kJ/mol / (1000 J/1 mol) = 745 J/mol
Step 3: Convert the surface area to cm^2 and calculate the surface energy.
Surface Area (cm^2) = Side Length * Side Length = (3.3 x 10^-8 cm) * (3.3 x 10^-8 cm)
Surface Energy (J/cm^2) = Heat of Atomization (J/atom) / Surface Area (cm^2)
Surface Energy (J/cm^2) = 745 J/mol / [ (3.3 x 10^-8 cm) * (3.3 x 10^-8 cm) ]
Now you can calculate the final answer using a calculator or a software like Python.