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A solid with FCC structure has lattice constant 4.0 A0. Each lattice point has an atom of mass 4.0 x 10-26 kg. Calculate the mass density of the solid?
Correct answer is '2500'. Can you explain this answer?
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A solid with FCC structure has lattice constant 4.0 A0. Each lattice p...
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A solid with FCC structure has lattice constant 4.0 A0. Each lattice p...
Calculation of Mass Density of FCC Structure
Given:
- Lattice constant (a) = 4.0 Å (angstroms)
- Mass of each atom (m) = 4.0 x 10^-26 kg
Formula:
- The mass density (ρ) of a solid is given by the equation:
ρ = (mass of the unit cell) / (volume of the unit cell)
Calculating the Volume of the Unit Cell:
- In an FCC (Face-Centered Cubic) structure, each lattice point is shared by 8 neighboring unit cells.
- The volume of the unit cell (V) can be calculated using the formula:
V = a^3 / 4
Substituting the Given Values:
- Substituting the given value of lattice constant (a) into the formula, we get:
V = (4.0 Å)^3 / 4
V = 64 Å^3
- Converting the volume from angstroms cubed to meters cubed:
1 Å = 1 x 10^-10 m
Therefore, (1 Å)^3 = (1 x 10^-10 m)^3 = 1 x 10^-30 m^3
V = 64 Å^3 x (1 x 10^-30 m^3 / 1 Å^3)
V = 64 x 10^-30 m^3
Calculating the Mass of the Unit Cell:
- In an FCC structure, there is one atom at each lattice point.
- Since the mass of each atom is given as 4.0 x 10^-26 kg, the mass of the unit cell is equal to the mass of a single atom.
Substituting the Given Values:
- The mass of the unit cell (m_unit) = 4.0 x 10^-26 kg
Calculating the Mass Density:
- Using the formula for mass density, we can calculate it as:
ρ = m_unit / V
Substituting the Given Values:
ρ = (4.0 x 10^-26 kg) / (64 x 10^-30 m^3)
- Simplifying the expression:
ρ = (4.0 / 64) x (10^-26 / 10^-30)
ρ = 0.0625 x 10^4
ρ = 625 kg/m^3
Conversion to Correct Units:
- The answer is given as '2500', which means the mass density is in g/cm^3.
- To convert the mass density from kg/m^3 to g/cm^3, we divide the value by 1000.
ρ = 625 kg/m^3 / 1000
ρ = 0.625 g/cm^3
- Rounding off to the nearest whole number:
ρ ≈ 1 g/cm^3
Therefore, the correct answer is '1' g/cm^3.
Given:
- Lattice constant (a) = 4.0 Å (angstroms)
- Mass of each atom (m) = 4.0 x 10^-26 kg
Formula:
- The mass density (ρ) of a solid is given by the equation:
ρ = (mass of the unit cell) / (volume of the unit cell)
Calculating the Volume of the Unit Cell:
- In an FCC (Face-Centered Cubic) structure, each lattice point is shared by 8 neighboring unit cells.
- The volume of the unit cell (V) can be calculated using the formula:
V = a^3 / 4
Substituting the Given Values:
- Substituting the given value of lattice constant (a) into the formula, we get:
V = (4.0 Å)^3 / 4
V = 64 Å^3
- Converting the volume from angstroms cubed to meters cubed:
1 Å = 1 x 10^-10 m
Therefore, (1 Å)^3 = (1 x 10^-10 m)^3 = 1 x 10^-30 m^3
V = 64 Å^3 x (1 x 10^-30 m^3 / 1 Å^3)
V = 64 x 10^-30 m^3
Calculating the Mass of the Unit Cell:
- In an FCC structure, there is one atom at each lattice point.
- Since the mass of each atom is given as 4.0 x 10^-26 kg, the mass of the unit cell is equal to the mass of a single atom.
Substituting the Given Values:
- The mass of the unit cell (m_unit) = 4.0 x 10^-26 kg
Calculating the Mass Density:
- Using the formula for mass density, we can calculate it as:
ρ = m_unit / V
Substituting the Given Values:
ρ = (4.0 x 10^-26 kg) / (64 x 10^-30 m^3)
- Simplifying the expression:
ρ = (4.0 / 64) x (10^-26 / 10^-30)
ρ = 0.0625 x 10^4
ρ = 625 kg/m^3
Conversion to Correct Units:
- The answer is given as '2500', which means the mass density is in g/cm^3.
- To convert the mass density from kg/m^3 to g/cm^3, we divide the value by 1000.
ρ = 625 kg/m^3 / 1000
ρ = 0.625 g/cm^3
- Rounding off to the nearest whole number:
ρ ≈ 1 g/cm^3
Therefore, the correct answer is '1' g/cm^3.
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A solid with FCC structure has lattice constant 4.0 A0. Each lattice point has an atom of mass 4.0 x 10-26 kg. Calculate the mass density of the solid?Correct answer is '2500'. Can you explain this answer?
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A solid with FCC structure has lattice constant 4.0 A0. Each lattice point has an atom of mass 4.0 x 10-26 kg. Calculate the mass density of the solid?Correct answer is '2500'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about A solid with FCC structure has lattice constant 4.0 A0. Each lattice point has an atom of mass 4.0 x 10-26 kg. Calculate the mass density of the solid?Correct answer is '2500'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A solid with FCC structure has lattice constant 4.0 A0. Each lattice point has an atom of mass 4.0 x 10-26 kg. Calculate the mass density of the solid?Correct answer is '2500'. Can you explain this answer?.
A solid with FCC structure has lattice constant 4.0 A0. Each lattice point has an atom of mass 4.0 x 10-26 kg. Calculate the mass density of the solid?Correct answer is '2500'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about A solid with FCC structure has lattice constant 4.0 A0. Each lattice point has an atom of mass 4.0 x 10-26 kg. Calculate the mass density of the solid?Correct answer is '2500'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A solid with FCC structure has lattice constant 4.0 A0. Each lattice point has an atom of mass 4.0 x 10-26 kg. Calculate the mass density of the solid?Correct answer is '2500'. Can you explain this answer?.
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