Concept explainers
(a)
Interpretation:
The hybridization of carbon atoms in carbon nanotubes, and the hybridization of boron and nitrogen atoms in boron nitride nanotubes have to be given.
(a)
Answer to Problem 8.31CE
The hybridization of carbon atoms in carbon nanotubes is
The hybridization of boron atoms in boron nitride nanotubes is
The hybridization of nitrogen atoms in boron nitride nanotubes is
Explanation of Solution
Carbon nanotubes are one-dimensional nanomaterial with density ranging from
Boron nitride nanotubes are a polymorph of boron nitride. They have similar structures to that of carbon nanotubes except that boron and nitride atoms in boron nitride nanotubes replace carbon atoms. Boron nitride nanotube is an electrical insulator. The boron and nitrogen atoms in boron nitride nanotubes are
(b)
Interpretation:
The number of hexagons that must be strung together around the circumference of a nanotube has to be given.
(b)
Explanation of Solution
Each unit in the given nanotube contains two hexagons, therefore, sixteen hexagons per circumference. The number of hexagons that must be strung together around the circumference of a nanotube is eight.
(c)
Interpretation:
The reason why the hydrogenation of Buckminsterfullerene stops at a certain point has to be explained.
(c)
Explanation of Solution
In buckminsterfullerene, the carbon atoms are planar and it is
(d)
Interpretation:
The structure of buckminsterfullerene has to be explained and the reason why boron nitride cannot form spheres has to be given.
(d)
Explanation of Solution
Buckminsterfullerene is a type of fullerene with a formula
The spherical structures require the formation of five-member rings. Boron nitride cannot form these rings because they require high-energy boron-boron or nitrogen-nitrogen bonds.
(e)
Interpretation:
The density of the cubic boron nitride has to be calculated.
(e)
Answer to Problem 8.31CE
The density of the cubic boron nitride is
Explanation of Solution
Given,
Edge length of the unit cell is
The number of atoms in the unit cell of face-centered cubic cell is four.
The mass of four atoms in the unit cell is calculated from the molar mass of boron nitride and
Mass=
The volume of the cubic unit cell is the length of the edge raised to its third power. The volume is calculated as,
The density is calculated as,
The density of the cubic boron nitride is
(f)
Interpretation:
The form of boron nitride that is favored at high pressures has to be given.
(f)
Answer to Problem 8.31CE
At high pressures, the cubic form of boron nitride is more favored.
Explanation of Solution
Cubic boron nitride is formed by high pressure, high temperature treatment of hexagonal boron nitride.
Cubic form of boron nitride is analogue to structure of diamond.
Hexagonal form of boron nitride is analogue to structure of graphite.
At high pressures, the cubic form of boron nitride is more favored since it is analogous to the structure of diamond.
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