(a) Sketch, in a cubic unit cell, a [111] and a [112] lattice direction. (b) Use a trigonometric calculation to determine the an
gle between these two directions. (c) Use Equation 3.3 to determine the angle between these two directions.
1 answer:
Answer and Explanation:
a) The direction is shown in the cube diagram attached to this solution.
b) the angle between two planes (h₁, k₁, l₁) and (h₂, k₂, l₂) is given by the formula,
Cos Φ = (h₁h₂ + k₁k₂ + l₁)/√((h₁² + k₁² + l₁²)(h₂² + k₂² + l₂²))
For (111) and (112)
Cos Φ = (1.1 + 1.1 + 1.2)/√((1² + 1² + 1²)(1² + 1² + 2²))
Cos Φ = (1 + 1 + 2)/√((1+1+1)(1+1+4))
Cos Φ = 4/√(3×6)
Cos Φ = 4/√18
Φ = cos⁻¹ (4/√18) = 19.56°
c) equation 3.3 is missing from the question, I would be back to provide the answers to that as soon as the equation is provided!
Hope this Helps!!
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Answer: (C) conservation of matter
Solution: Law of conservation of matter or mass states that' total mass of the reactants should always be equal to the total mass of the product that is the total mass is remained conserved in a chemical reaction.
A balanced chemical equation always follow this law.
For example:
Mass of hydrogen = 1 g/mol
Mass of Oxygen = 16 g/mol
Total mass on the reactants = 2(2×1)+(2×16)= 36g/mol
Total mass on the product side = 2[(2×1) +16] = 36 g/mol
As,
Mass on reactant side = Mass on the product side
Therefore, a balanced chemical reaction follows Law of Conservation of mass.
Each element or compound has a molar mass, which is calculated by multiplying the atomic mass of each element by the amount of atoms of that element, and summing the results of each element. The molar mass is measured in g/mol. So you divide the mass in grams by the molar mass to get the amount of moles.
Example:
There are 5g of water.
Calculate the amount of moles.
The water's formula is H2O, so the molar mass of it is
g/mol.
The amount of moles is:
5g ÷ 18g/mol ~ 0.28mol