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If an element crystallizes as a simple cube, what is the volume of an element provided its density is 1.5 g/cm3 and atomic mass of the element is 63?
- a)69.7 x 10 -23 cm3
- b)6.97 x 10 -23 cm3
- c)63 x 10 -23 cm3
- d)5.97 x 10 -23 cm3
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
If an element crystallizes as a simple cube, what is the volume of an ...
Given:
Density of the element = 1.5 g/cm³
Atomic mass of the element = 63
To find:
Volume of the element if it crystallizes as a simple cube
Solution:
1. Calculation of the edge length of the cube:
In a simple cube, the atoms are arranged in a cubic lattice with one atom at each corner of the cube.
The edge length of the cube can be calculated using the formula:
a = (4/3 πr³)^(1/3)
where,
a = edge length of the cube
r = radius of the atom = (atomic mass/molar mass)^(1/3)
Here,
molar mass of the element = atomic mass
r = (63/6.022 x 10²³)^(1/3) = 1.27 x 10^-8 cm
Therefore,
a = (4/3 π(1.27 x 10^-8)³)^(1/3) = 3.57 x 10^-8 cm
2. Calculation of the volume of the cube:
The volume of the cube can be calculated using the formula:
V = a³
where,
V = volume of the cube
a = edge length of the cube
Substituting the value of a, we get:
V = (3.57 x 10^-8)³ = 6.97 x 10^-23 cm³
3. Comparison with the given options:
The calculated volume of the element is 6.97 x 10^-23 cm³, which matches with option (B).
Therefore, the correct answer is option (B) 6.97 x 10^-23 cm³.
Density of the element = 1.5 g/cm³
Atomic mass of the element = 63
To find:
Volume of the element if it crystallizes as a simple cube
Solution:
1. Calculation of the edge length of the cube:
In a simple cube, the atoms are arranged in a cubic lattice with one atom at each corner of the cube.
The edge length of the cube can be calculated using the formula:
a = (4/3 πr³)^(1/3)
where,
a = edge length of the cube
r = radius of the atom = (atomic mass/molar mass)^(1/3)
Here,
molar mass of the element = atomic mass
r = (63/6.022 x 10²³)^(1/3) = 1.27 x 10^-8 cm
Therefore,
a = (4/3 π(1.27 x 10^-8)³)^(1/3) = 3.57 x 10^-8 cm
2. Calculation of the volume of the cube:
The volume of the cube can be calculated using the formula:
V = a³
where,
V = volume of the cube
a = edge length of the cube
Substituting the value of a, we get:
V = (3.57 x 10^-8)³ = 6.97 x 10^-23 cm³
3. Comparison with the given options:
The calculated volume of the element is 6.97 x 10^-23 cm³, which matches with option (B).
Therefore, the correct answer is option (B) 6.97 x 10^-23 cm³.
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Community Answer
If an element crystallizes as a simple cube, what is the volume of an ...
1st calculate the edgelength by the formula of density and wd know that d=m/v put the relation nd u will get the answer
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If an element crystallizes as a simple cube, what is the volume of an element provided its density is 1.5 g/cm3and atomic mass of the element is 63?a)69.7 x 10-23cm3b)6.97 x 10-23cm3c)63 x 10-23cm3d)5.97 x 10-23cm3Correct answer is option 'B'. Can you explain this answer?
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If an element crystallizes as a simple cube, what is the volume of an element provided its density is 1.5 g/cm3and atomic mass of the element is 63?a)69.7 x 10-23cm3b)6.97 x 10-23cm3c)63 x 10-23cm3d)5.97 x 10-23cm3Correct answer is option 'B'. 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 If an element crystallizes as a simple cube, what is the volume of an element provided its density is 1.5 g/cm3and atomic mass of the element is 63?a)69.7 x 10-23cm3b)6.97 x 10-23cm3c)63 x 10-23cm3d)5.97 x 10-23cm3Correct answer is option 'B'. 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 If an element crystallizes as a simple cube, what is the volume of an element provided its density is 1.5 g/cm3and atomic mass of the element is 63?a)69.7 x 10-23cm3b)6.97 x 10-23cm3c)63 x 10-23cm3d)5.97 x 10-23cm3Correct answer is option 'B'. Can you explain this answer?.
If an element crystallizes as a simple cube, what is the volume of an element provided its density is 1.5 g/cm3and atomic mass of the element is 63?a)69.7 x 10-23cm3b)6.97 x 10-23cm3c)63 x 10-23cm3d)5.97 x 10-23cm3Correct answer is option 'B'. 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 If an element crystallizes as a simple cube, what is the volume of an element provided its density is 1.5 g/cm3and atomic mass of the element is 63?a)69.7 x 10-23cm3b)6.97 x 10-23cm3c)63 x 10-23cm3d)5.97 x 10-23cm3Correct answer is option 'B'. 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 If an element crystallizes as a simple cube, what is the volume of an element provided its density is 1.5 g/cm3and atomic mass of the element is 63?a)69.7 x 10-23cm3b)6.97 x 10-23cm3c)63 x 10-23cm3d)5.97 x 10-23cm3Correct answer is option 'B'. Can you explain this answer?.
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