(a) Diamond and graphite are both forms of carbon. The difference in hardness is due to the way the carbon atoms are bonded together. In diamond, each carbon atom is bonded to four other carbon atoms in a tetrahedral structure, which makes it extremely hard. In graphite, each carbon atom is bonded to three other carbon atoms in a layered structure, which allows the layers to slide over each other, making it soft.

(b) The (100) plane is absent in the X-ray diffraction pattern of the BCC (Body Centered Cubic) structure because the atomic planes in this structure do not satisfy the Bragg's condition for diffraction. The Bragg's condition states that diffraction occurs when the path difference between the incident and reflected X-rays is an integral multiple of the wavelength. In the BCC structure, the atoms on the (100) plane do not satisfy this condition.

(c) There is no Face Centered Tetragonal lattice because in a Face Centered Tetragonal lattice, the unit cell would have atoms at each corner and in the center of each face, but the lengths of the cell edges along the x, y, and z axes would not be equal. This is not possible because it would violate the requirement for a lattice to have translational symmetry in all directions.

(d) Larger size anode has less corrosion because the rate of corrosion is inversely proportional to the surface area of the anode. The larger the anode, the lower the current density, and hence the lower the rate of corrosion.

(e) A regular 2-D pentagon lattice is not possible because a regular pentagon does not tessellate, or fill space, without leaving gaps. This is a requirement for a lattice structure. The only regular polygons that can tessellate in 2-D are triangles, squares, and hexagons.

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(a) Diamond and graphite are both forms of carbon. The difference in hardness is due to the way the carbon atoms are bonded together. In diamond, each carbon atom is bonded to four other carbon atoms in a tetrahedral structure, which makes it extremely hard. In graphite, each carbon atom is bonded to three other carbon atoms in a layered structure, which allows the layers to slide over each other, making it soft.

(b) The (100) plane is absent in the X-ray diffraction pattern of the BCC (Body Centered Cubic) structure because the atomic planes in this structure do not satisfy the Bragg's condition for diffraction. The Bragg's condition states that diffraction occurs when the path difference between the incident and reflected X-rays is an integral multiple of the wavelength. In the BCC structure, the atoms on the (100) plane do not satisfy this condition.

(c) There is no Face Centered Tetragonal lattice because in a Face Centered Tetragonal lattice, the unit cell would have atoms at each corner and in the center of each face, but the lengths of the cell edges along the x, y, and z axes would not be equal. This is not possible because it would violate the requirement for a lattice to have translational symmetry in all directions.

(d) Larger size anode has less corrosion because the rate of corrosion is inversely proportional to the surface area of the anode. The larger the anode, the lower the current density, and hence the lower the rate of corrosion.

(e) A regular 2-D pentagon lattice is not possible because a regular pentagon does not tessellate, or fill space, without leaving gaps. This is a requirement for a lattice structure. The only regular polygons that can tessellate in 2-D are triangles, squares, and hexagons.

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(a) Diamond and graphite are both forms of carbon. The difference in hardness is due to the way the carbon atoms are bonded together. In diamond, each carbon atom is bonded to four other carbon atoms in a tetrahedral structure, which makes it extremely hard. In graphite, each carbon atom is bonded to three other carbon atoms in a layered structure, which allows the layers to slide over each other, making it soft.

(b) The (100) plane is absent in the X-ray diffraction pattern of the BCC (Body Centered Cubic) structure because the atomic planes in this structure do not satisfy the Bragg's condition for diffraction. The Bragg's condition states that diffraction occurs when the path difference between the incident and reflected X-rays is an integral multiple of the wavelength. In the BCC structure, the atoms on the (100) plane do not satisfy this condition.

(c) There is no Face Centered Tetragonal lattice because in a Face Centered Tetragonal lattice, the unit cell would have atoms at each corner and in the center of each face, but the lengths of the cell edges along the x, y, and z axes would not be equal. This is not possible because it would violate the requirement for a lattice to have translational symmetry in all directions.

(d) Larger size anode has less corrosion because the rate of corrosion is inversely proportional to the surface area of the anode. The larger the anode, the lower the current density, and hence the lower the rate of corrosion.

(e) A regular 2-D pentagon lattice is not possible because a regular pentagon does not tessellate, or fill space, without leaving gaps. This is a requirement for a lattice structure. The only regular polygons that can tessellate in 2-D are triangles, squares, and hexagons.

Diamond is hard, but graphite is soft.(b) (100) plane is absent in the X-ray diffraction pattern of the BCC structure.(c) There is no Face Centered Tetragonal lattice.(d) Larger size anode has less corrosion.(e) A regular 2-D pentagon lattice is not possible.

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