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Potassium has a bcc structure with nearest neighbour distance 4.52 Å . Its atomic weight is 39, its density will be :
- a)0.91 kg m-3
- b)0.852 kg m-3
- c)852 kg m-3
- d)910 kg m-3
Correct answer is option 'D'. Can you explain this answer?
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Potassium has a bcc structure with nearest neighbour distance 4.52 &Ar...
Å and atomic radius 2.31 Å.
To calculate the packing fraction, we need to first determine the volume of one potassium atom. The volume of an atom can be approximated as a sphere with a radius equal to the atomic radius, so the volume of one potassium atom is:
V_atom = 4/3 * π * r^3
V_atom = 4/3 * π * (2.31 Å)^3
V_atom = 47.6 Å^3
Next, we need to determine the volume of the unit cell. The bcc unit cell has a cube shape, with the atom located at the center and eight atoms at the corners of the cube. The nearest neighbour distance of 4.52 Å corresponds to the diagonal of the cube, so the length of one edge of the cube is:
a = 4.52 / sqrt(3)
a = 2.61 Å
The volume of the unit cell is then:
V_cell = a^3
V_cell = (2.61 Å)^3
V_cell = 18.8 Å^3
Finally, we can calculate the packing fraction as the ratio of the total volume of the atoms in the unit cell to the volume of the unit cell:
packing fraction = n * V_atom / V_cell
where n is the number of atoms in the unit cell. For bcc structures, there are two atoms in the unit cell (one at the center and one at the corner of the cube). Therefore:
packing fraction = 2 * 47.6 Å^3 / 18.8 Å^3
packing fraction = 1.61
The packing fraction for bcc potassium is 1.61, which means that the atoms occupy about 61% of the total volume of the unit cell.
To calculate the packing fraction, we need to first determine the volume of one potassium atom. The volume of an atom can be approximated as a sphere with a radius equal to the atomic radius, so the volume of one potassium atom is:
V_atom = 4/3 * π * r^3
V_atom = 4/3 * π * (2.31 Å)^3
V_atom = 47.6 Å^3
Next, we need to determine the volume of the unit cell. The bcc unit cell has a cube shape, with the atom located at the center and eight atoms at the corners of the cube. The nearest neighbour distance of 4.52 Å corresponds to the diagonal of the cube, so the length of one edge of the cube is:
a = 4.52 / sqrt(3)
a = 2.61 Å
The volume of the unit cell is then:
V_cell = a^3
V_cell = (2.61 Å)^3
V_cell = 18.8 Å^3
Finally, we can calculate the packing fraction as the ratio of the total volume of the atoms in the unit cell to the volume of the unit cell:
packing fraction = n * V_atom / V_cell
where n is the number of atoms in the unit cell. For bcc structures, there are two atoms in the unit cell (one at the center and one at the corner of the cube). Therefore:
packing fraction = 2 * 47.6 Å^3 / 18.8 Å^3
packing fraction = 1.61
The packing fraction for bcc potassium is 1.61, which means that the atoms occupy about 61% of the total volume of the unit cell.
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Potassium has a bcc structure with nearest neighbour distance 4.52 Å . Its atomic weight is 39, its density will be :a)0.91 kg m-3 b)0.852 kg m-3 c)852 kg m-3 d)910 kg m-3Correct answer is option 'D'. Can you explain this answer? for Class 12 2025 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about Potassium has a bcc structure with nearest neighbour distance 4.52 Å . Its atomic weight is 39, its density will be :a)0.91 kg m-3 b)0.852 kg m-3 c)852 kg m-3 d)910 kg m-3Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 12 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Potassium has a bcc structure with nearest neighbour distance 4.52 Å . Its atomic weight is 39, its density will be :a)0.91 kg m-3 b)0.852 kg m-3 c)852 kg m-3 d)910 kg m-3Correct answer is option 'D'. Can you explain this answer?.
Potassium has a bcc structure with nearest neighbour distance 4.52 Å . Its atomic weight is 39, its density will be :a)0.91 kg m-3 b)0.852 kg m-3 c)852 kg m-3 d)910 kg m-3Correct answer is option 'D'. Can you explain this answer? for Class 12 2025 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about Potassium has a bcc structure with nearest neighbour distance 4.52 Å . Its atomic weight is 39, its density will be :a)0.91 kg m-3 b)0.852 kg m-3 c)852 kg m-3 d)910 kg m-3Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 12 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Potassium has a bcc structure with nearest neighbour distance 4.52 Å . Its atomic weight is 39, its density will be :a)0.91 kg m-3 b)0.852 kg m-3 c)852 kg m-3 d)910 kg m-3Correct answer is option 'D'. Can you explain this answer?.
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Potassium has a bcc structure with nearest neighbour distance 4.52 Å . Its atomic weight is 39, its density will be :a)0.91 kg m-3 b)0.852 kg m-3 c)852 kg m-3 d)910 kg m-3Correct answer is option 'D'. Can you explain this answer?, a detailed solution for Potassium has a bcc structure with nearest neighbour distance 4.52 Å . Its atomic weight is 39, its density will be :a)0.91 kg m-3 b)0.852 kg m-3 c)852 kg m-3 d)910 kg m-3Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of Potassium has a bcc structure with nearest neighbour distance 4.52 Å . Its atomic weight is 39, its density will be :a)0.91 kg m-3 b)0.852 kg m-3 c)852 kg m-3 d)910 kg m-3Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
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