calculate the surface energy of 100 surface of niobium. The enthalpy of atomization of niobium is 745 kj/mol. express anser inunits of j/cm^2
2.8*10^-4
It's wrong btw
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 (half for each surface)
Surface energy (100) =1/2 * 4 * Atoms density * Bond Energy = 0.00028364488 J/cm2
so wrong
try ivos idea
To calculate the surface energy of niobium, we need to know the enthalpy of atomization and the surface area of 100 niobium atoms.
1. Convert the enthalpy of atomization from kilojoules per mole (kJ/mol) to joules per atom. Since 1 mol contains Avogadro's number (6.022 x 10^23) of atoms, we divide the enthalpy by Avogadro's number:
Enthalpy per atom = Enthalpy of atomization / Avogadro's number
Enthalpy per atom = 745 kJ/mol / (6.022 x 10^23 atoms/mol)
2. Calculate the surface area of 100 niobium atoms. The surface area of a single atom can be considered as a circle with a diameter equal to the atomic radius. The atomic radius of niobium is approximately 0.143 nm (nanometers).
Surface area of 1 niobium atom = π * (atomic radius)^2
Surface area of 1 niobium atom = 3.14 * (0.143 nm)^2
Surface area of 100 niobium atoms = 100 * Surface area of 1 niobium atom
3. Finally, calculate the surface energy using the equation:
Surface energy = Enthalpy per atom / Surface area of 100 niobium atoms
Ensure the units are converted appropriately. Since the area is in square centimeters (cm^2), we need to convert the atomic radius from nanometers to centimeters.
Surface energy = (Enthalpy per atom in J) / (Surface area of 100 niobium atoms in cm^2)
Plug in the values to get your answer in Joules per square centimeter (J/cm^2).