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Aluminium crystallises in a face-centred cubic lattice. The edge length of the unit cell of aluminium is 4.05 x 10-10m. What is the density of aluminium? (Atomic mass of Al=27)
- a)2700 kg m-3
- b)3000 kg m-3
- c)2400 kg m-3
- d)2100 kg m-3
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Aluminium crystallises in a face-centred cubic lattice. The edge lengt...
Given,
Atomic mass (M)=27 amu
For FCC structure, Z=4
Avogadro’s number (N0) = 6.02 x 1023
Edge length of the Al unit cell (a)= 4.05 x 10-10m
The density of aluminium (ρ) = (Z x M)/(a3 X N0)
= (4 x 27)/((4.05 x 10-10) 3 x 6.02 x 1023)
= 2700 kg m-3.
Atomic mass (M)=27 amu
For FCC structure, Z=4
Avogadro’s number (N0) = 6.02 x 1023
Edge length of the Al unit cell (a)= 4.05 x 10-10m
The density of aluminium (ρ) = (Z x M)/(a3 X N0)
= (4 x 27)/((4.05 x 10-10) 3 x 6.02 x 1023)
= 2700 kg m-3.
Most Upvoted Answer
Aluminium crystallises in a face-centred cubic lattice. The edge lengt...
Given,
Atomic mass (M)=27 amu
For FCC structure, Z=4
Avogadro’s number (N0) = 6.02 x 1023
Edge length of the Al unit cell (a)= 4.05 x 10-10m
The density of aluminium (ρ) = (Z x M)/(a3 X N0)
= (4 x 27)/((4.05 x 10-10) 3 x 6.02 x 1023)
= 2700 kg m-3.
Atomic mass (M)=27 amu
For FCC structure, Z=4
Avogadro’s number (N0) = 6.02 x 1023
Edge length of the Al unit cell (a)= 4.05 x 10-10m
The density of aluminium (ρ) = (Z x M)/(a3 X N0)
= (4 x 27)/((4.05 x 10-10) 3 x 6.02 x 1023)
= 2700 kg m-3.
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Community Answer
Aluminium crystallises in a face-centred cubic lattice. The edge lengt...
Given:
- Aluminium crystallises in a face-centred cubic lattice.
- The edge length of the unit cell of aluminium is 4.05 x 10^-10 m.
- Atomic mass of Al = 27
To find:
Density of aluminium
Explanation:
Step 1: Calculate the volume of the unit cell
- In a face-centred cubic (FCC) lattice, there are 4 atoms per unit cell.
- The face-centred cubic lattice has atoms at each corner of the cube and also at the center of each face.
- The volume of the unit cell can be calculated using the formula: Volume = a^3, where 'a' is the edge length of the unit cell.
Given: a = 4.05 x 10^-10 m
Volume of the unit cell = (4.05 x 10^-10 m)^3
Step 2: Calculate the mass of the unit cell
- Since there are 4 atoms per unit cell and the atomic mass of Al is 27, the total mass of the unit cell can be calculated as follows:
Mass of the unit cell = 4 x (Atomic mass of Al)
Given: Atomic mass of Al = 27
Mass of the unit cell = 4 x 27
Step 3: Calculate the density of aluminium
- Density is defined as the mass divided by the volume. Therefore, the density of aluminium can be calculated using the formula:
Density = Mass of the unit cell / Volume of the unit cell
Substituting the values:
Density = (4 x 27) / (4.05 x 10^-10 m)^3
Simplifying the expression:
Density = 27 / (4.05 x 10^-10 m)^3
Converting the exponent to positive:
Density = 27 / (4.05 x 10^10 m)^3
Calculating the density:
Density = 2700 kg/m^3
Conclusion:
The density of aluminium is 2700 kg/m^3. Therefore, the correct answer is option A.
- Aluminium crystallises in a face-centred cubic lattice.
- The edge length of the unit cell of aluminium is 4.05 x 10^-10 m.
- Atomic mass of Al = 27
To find:
Density of aluminium
Explanation:
Step 1: Calculate the volume of the unit cell
- In a face-centred cubic (FCC) lattice, there are 4 atoms per unit cell.
- The face-centred cubic lattice has atoms at each corner of the cube and also at the center of each face.
- The volume of the unit cell can be calculated using the formula: Volume = a^3, where 'a' is the edge length of the unit cell.
Given: a = 4.05 x 10^-10 m
Volume of the unit cell = (4.05 x 10^-10 m)^3
Step 2: Calculate the mass of the unit cell
- Since there are 4 atoms per unit cell and the atomic mass of Al is 27, the total mass of the unit cell can be calculated as follows:
Mass of the unit cell = 4 x (Atomic mass of Al)
Given: Atomic mass of Al = 27
Mass of the unit cell = 4 x 27
Step 3: Calculate the density of aluminium
- Density is defined as the mass divided by the volume. Therefore, the density of aluminium can be calculated using the formula:
Density = Mass of the unit cell / Volume of the unit cell
Substituting the values:
Density = (4 x 27) / (4.05 x 10^-10 m)^3
Simplifying the expression:
Density = 27 / (4.05 x 10^-10 m)^3
Converting the exponent to positive:
Density = 27 / (4.05 x 10^10 m)^3
Calculating the density:
Density = 2700 kg/m^3
Conclusion:
The density of aluminium is 2700 kg/m^3. Therefore, the correct answer is option A.
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Aluminium crystallises in a face-centred cubic lattice. The edge length of the unit cell of aluminium is 4.05 x 10-10m. What is the density of aluminium? (Atomic mass of Al=27)a)2700 kg m-3b)3000 kg m-3c)2400 kg m-3d)2100 kg m-3Correct answer is option 'A'. Can you explain this answer?
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Aluminium crystallises in a face-centred cubic lattice. The edge length of the unit cell of aluminium is 4.05 x 10-10m. What is the density of aluminium? (Atomic mass of Al=27)a)2700 kg m-3b)3000 kg m-3c)2400 kg m-3d)2100 kg m-3Correct answer is option 'A'. Can you explain this answer? for Chemistry 2024 is part of Chemistry preparation. The Question and answers have been prepared according to the Chemistry exam syllabus. Information about Aluminium crystallises in a face-centred cubic lattice. The edge length of the unit cell of aluminium is 4.05 x 10-10m. What is the density of aluminium? (Atomic mass of Al=27)a)2700 kg m-3b)3000 kg m-3c)2400 kg m-3d)2100 kg m-3Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Chemistry 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Aluminium crystallises in a face-centred cubic lattice. The edge length of the unit cell of aluminium is 4.05 x 10-10m. What is the density of aluminium? (Atomic mass of Al=27)a)2700 kg m-3b)3000 kg m-3c)2400 kg m-3d)2100 kg m-3Correct answer is option 'A'. Can you explain this answer?.
Aluminium crystallises in a face-centred cubic lattice. The edge length of the unit cell of aluminium is 4.05 x 10-10m. What is the density of aluminium? (Atomic mass of Al=27)a)2700 kg m-3b)3000 kg m-3c)2400 kg m-3d)2100 kg m-3Correct answer is option 'A'. Can you explain this answer? for Chemistry 2024 is part of Chemistry preparation. The Question and answers have been prepared according to the Chemistry exam syllabus. Information about Aluminium crystallises in a face-centred cubic lattice. The edge length of the unit cell of aluminium is 4.05 x 10-10m. What is the density of aluminium? (Atomic mass of Al=27)a)2700 kg m-3b)3000 kg m-3c)2400 kg m-3d)2100 kg m-3Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Chemistry 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Aluminium crystallises in a face-centred cubic lattice. The edge length of the unit cell of aluminium is 4.05 x 10-10m. What is the density of aluminium? (Atomic mass of Al=27)a)2700 kg m-3b)3000 kg m-3c)2400 kg m-3d)2100 kg m-3Correct answer is option 'A'. Can you explain this answer?.
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