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A metal X has a BCC structure with nearest neighbor distance 365.9 pm. What is metal X if its density is 1.0016 g cm-3?
- a)Aluminum
- b)Magnesium
- c)Sodium
- d)Potassium
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A metal X has a BCC structure with nearest neighbor distance 365.9 pm....
Given,
Nearest neighbor distance (d) = 365.9 pm
Density (ρ) = 1.51 g cm-3
For the BCC structure, nearest neighbor distance (d) is related to the edge length (a) as d=
Or a=
x d = 2/1.732 x 365.9 = 422.5 pm
For BCC structure, Z=2
We know, (ρ) = (Z x M)/(a3 x N0)
Or M = (ρ x a3 x N0)/Z
= (1.0016 x 106 x (422.5 x 10-12)3 x 6.02 x 1023)/2
= 23 amu
Therefore, the given metal X is Sodium.
Nearest neighbor distance (d) = 365.9 pm
Density (ρ) = 1.51 g cm-3
For the BCC structure, nearest neighbor distance (d) is related to the edge length (a) as d=
Or a=
x d = 2/1.732 x 365.9 = 422.5 pmFor BCC structure, Z=2
We know, (ρ) = (Z x M)/(a3 x N0)
Or M = (ρ x a3 x N0)/Z
= (1.0016 x 106 x (422.5 x 10-12)3 x 6.02 x 1023)/2
= 23 amu
Therefore, the given metal X is Sodium.
Most Upvoted Answer
A metal X has a BCC structure with nearest neighbor distance 365.9 pm....
Nearest Neighbor Distance and Density
Nearest Neighbor Distance:
The nearest neighbor distance is the distance between the centers of two adjacent atoms in a crystal lattice.
BCC Structure:
The Body-Centered Cubic (BCC) structure is a type of crystal lattice structure. In this structure, each atom is located at the corner of a cube and there is an additional atom at the center of the cube.
Density:
Density is defined as the mass per unit volume of a substance. It is calculated by dividing the mass of the substance by its volume.
Calculating Density:
To calculate the density of a material, we need to know its mass and volume. The formula for density is:
Density = Mass / Volume
Given Information:
- Nearest neighbor distance in metal X = 365.9 pm (picometers)
- Density of metal X = 1.0016 g cm-3 (grams per cubic centimeter)
Solution:
To determine the metal X, we need to compare the given nearest neighbor distance with the known values for different metals.
Step 1: Convert the nearest neighbor distance from picometers to centimeters.
1 pm = 1 × 10^-12 cm
Nearest neighbor distance = 365.9 pm × (1 × 10^-12 cm / 1 pm) = 3.659 × 10^-8 cm
Step 2: Calculate the volume of the unit cell in the BCC structure.
In a BCC structure, there are two atoms per unit cell, one at the corner and one at the center.
Volume of the unit cell = (4/3) × π × (Nearest neighbor distance / 2)^3
Volume of the unit cell = (4/3) × π × (3.659 × 10^-8 cm / 2)^3 = 9.989 × 10^-23 cm^3
Step 3: Calculate the mass of the unit cell.
The mass of the unit cell can be obtained by multiplying the volume of the unit cell by the density of metal X.
Mass of the unit cell = Volume of the unit cell × Density
Mass of the unit cell = 9.989 × 10^-23 cm^3 × 1.0016 g cm-3 = 9.999 × 10^-23 g
Step 4: Compare the mass of the unit cell with the known values for different metals.
By comparing the mass of the unit cell with the known values for different metals, we find that the closest match is sodium (Na), which has a mass of 9.999 × 10^-23 g.
Therefore, the metal X is sodium (Na).
Nearest Neighbor Distance:
The nearest neighbor distance is the distance between the centers of two adjacent atoms in a crystal lattice.
BCC Structure:
The Body-Centered Cubic (BCC) structure is a type of crystal lattice structure. In this structure, each atom is located at the corner of a cube and there is an additional atom at the center of the cube.
Density:
Density is defined as the mass per unit volume of a substance. It is calculated by dividing the mass of the substance by its volume.
Calculating Density:
To calculate the density of a material, we need to know its mass and volume. The formula for density is:
Density = Mass / Volume
Given Information:
- Nearest neighbor distance in metal X = 365.9 pm (picometers)
- Density of metal X = 1.0016 g cm-3 (grams per cubic centimeter)
Solution:
To determine the metal X, we need to compare the given nearest neighbor distance with the known values for different metals.
Step 1: Convert the nearest neighbor distance from picometers to centimeters.
1 pm = 1 × 10^-12 cm
Nearest neighbor distance = 365.9 pm × (1 × 10^-12 cm / 1 pm) = 3.659 × 10^-8 cm
Step 2: Calculate the volume of the unit cell in the BCC structure.
In a BCC structure, there are two atoms per unit cell, one at the corner and one at the center.
Volume of the unit cell = (4/3) × π × (Nearest neighbor distance / 2)^3
Volume of the unit cell = (4/3) × π × (3.659 × 10^-8 cm / 2)^3 = 9.989 × 10^-23 cm^3
Step 3: Calculate the mass of the unit cell.
The mass of the unit cell can be obtained by multiplying the volume of the unit cell by the density of metal X.
Mass of the unit cell = Volume of the unit cell × Density
Mass of the unit cell = 9.989 × 10^-23 cm^3 × 1.0016 g cm-3 = 9.999 × 10^-23 g
Step 4: Compare the mass of the unit cell with the known values for different metals.
By comparing the mass of the unit cell with the known values for different metals, we find that the closest match is sodium (Na), which has a mass of 9.999 × 10^-23 g.
Therefore, the metal X is sodium (Na).
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Community Answer
A metal X has a BCC structure with nearest neighbor distance 365.9 pm....
Given,
Nearest neighbor distance (d) = 365.9 pm
Density (ρ) = 1.51 g cm-3
For the BCC structure, nearest neighbor distance (d) is related to the edge length (a) as d=
Or a=x d = 2/1.732 x 365.9 = 422.5 pm
For BCC structure, Z=2
We know, (ρ) = (Z x M)/(a3 x N0)
Or M = (ρ x a3 x N0)/Z
= (1.0016 x 106 x (422.5 x 10-12)3 x 6.02 x 1023)/2
= 23 amu
Therefore, the given metal X is Sodium.
Nearest neighbor distance (d) = 365.9 pm
Density (ρ) = 1.51 g cm-3
For the BCC structure, nearest neighbor distance (d) is related to the edge length (a) as d=
Or a=
x d = 2/1.732 x 365.9 = 422.5 pmFor BCC structure, Z=2
We know, (ρ) = (Z x M)/(a3 x N0)
Or M = (ρ x a3 x N0)/Z
= (1.0016 x 106 x (422.5 x 10-12)3 x 6.02 x 1023)/2
= 23 amu
Therefore, the given metal X is Sodium.
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A metal X has a BCC structure with nearest neighbor distance 365.9 pm. What is metal X if its density is 1.0016 g cm-3?a)Aluminumb)Magnesiumc)Sodiumd)PotassiumCorrect answer is option 'C'. Can you explain this answer?
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