Calculate the surface energy of the (100) surface of niobium. The enthalpy of atomization of niobium is 745 kJ/mole. Express your answer in units of J/cm2.
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cheat .3.091 x 10^-3 joules/cm2
To calculate the surface energy of a crystal surface, we need to use the following equation:
Surface Energy (γ) = (Enthalpy of Atomization) / (Surface Area)
To find the surface area of the (100) surface of niobium, we need to know the lattice constant (a) and the Miller indices. For the (100) surface, we can use the formula:
Surface Area = a^2
The lattice constant for niobium is approximately 0.329 nm or 3.29 Å.
Now, we can substitute the given values into the formula to calculate the surface energy:
1. Convert the enthalpy of atomization from kJ/mole to J/mole:
Enthalpy of Atomization = 745 kJ/mole = 745,000 J/mole
2. Calculate the surface area:
Surface Area = (0.329 nm)^2 = (0.329 x 10^-7 cm)^2 = 1.08 x 10^-14 cm^2
3. Substitute the values into the surface energy equation:
Surface Energy (γ) = (Enthalpy of Atomization) / (Surface Area)
Surface Energy (γ) = 745,000 J/mole / 1.08 x 10^-14 cm^2
4. Convert the result to J/cm^2:
Surface Energy (γ) = (745,000 J/mole) / (1.08 x 10^-14 cm^2) = 6.88 x 10^17 J/cm^2
Therefore, the surface energy of the (100) surface of niobium is approximately 6.88 x 10^17 J/cm^2.