(Thanks to Avnish of 12th standard, RKT College Ulhasnagar for reaching out to www.sciencedidi.com and asking doubts. We encourage students to come forward and feel free to share their questions, be it for exams or otherwise)
Q ) Differentiate between crystalline and amorphous solid.
Solids are all substances in which atoms are tightly packed but they can vastly differ in the way in which they atoms are arranged among themselves.
A crystalline solid has atoms arranged in a regular fashion, also referred to as long range order. On the other hand, an amorphous solid (also known as glass) has atoms having some short range order but no long range order. That means unlike a crystal, in amorphous solid there is no specific unit cell which can be repeated to get the entire arrangement.
(Source: https://www.researchgate.net/publication/322746543_Glass-to-crystal_transition_in_a_chiral_pharmaceutical_system/figures?lo=1)
The difference between the two can be seen via X-Ray Diffraction (XRD). The sharp peaks in XRD of crystalline solid corresponds to the regularity in the spacing between the atoms which causes the diffraction at a given specific angle (n x wavelength = 2 x atomic spacing x sin (angle-theta).
We can see that for amorphous solid there is are no sharp peaks, which means atomic spacing is not regular.
A lot of properties differ when the atomic arrangement changes even if the solid is composed of the same atoms.
Crystalline solids have a sharp melting point, generally higher than amorphous solid as more energy is needed to break the long range order. Amorphous solids have a range of melting point below the crystalline melting point, making it easy to mold and give shape.
2) Classify them as molecular, ionic, covalent or metallic solid. )Pb, MgF2, SO2 and Quartz)
Pb is lead, which is a metallic element so it is metallic solid.
MgF2 is composed of alkaline earth metal Magnesium which has low electronegativity and fluorine is a non-metal which has highest electronegativity (tendency to pull electrons towards itself in a bond). In such combinations, metals form cations (+) by giving electron and non metals form anions (-), hence Magnesium Difluoride is ionic solid.
SO2 generally is a gas molecule, so solidifying means basically to freeze it, making it a molecular solid.
Quartz is silicion dioxide in which silicon and oxygen are connected to each other over a long series of covalent bonds (by sharing electrons), so it is a covalent solid.
3) Find the number of atoms in FCC unit cell.
FCC stands for Face Centered Cubic unit cell.
(Source: https://www.researchgate.net/publication/322291448_Development_of_a_polycrystal_plasticity_simulation_tool_including_recrystallization_DRX_phenomena/figures?lo=1)
The above image a) can help visualize that the there are 6 faces of a cube with 6 atoms being shared between two adjacent unit cells. So the contribution of those 6 face centered atoms to one unit cell is 6/2 = 3.
There are 8 atoms in the corner, each of which is shared by 8 unit cells, four on the top and four in the bottom. So contribution of those 8 corner atoms to one unit cell is 8/8 = 1.
So there are 3 + 1 = 4 atoms in one unit cell of FCC.
4) What is a vacancy defect ?
In a perfect crystal, the arrangement of atoms should be very uniform. However perfection is unrealistic in atomic world as in our human world so there can be a defect called vacancy when an atom is ‘missing’ from the from the perfect periodic position, thereby creating strain and distortion to nearby atoms.
5) Calculate the number of unit cells in 0.3 g of a solid having density 8.5 g/cc and unit cell edge length 3.25 x 10^-8 cm.
First lets find the volume of one unit cell which is cubic in shape.
Volume of unit cell = (Edge length)^3 = (3.25 x 10^-8)^3 = 34.33 x 10^-24 cubic centimeter.
Volume occupied by 0.3 gram of solid = Mass/ density = 0.3/8.5 = 0.035 cubic centimeter.
Number of unit cells = Total volume/Volume of unit cell = 1.03 x 10^21 units
6) A compound crystallizes in BCC structure. What is it’s edge length of unit cell if the diameter of the atom is 120 picometer ?
BCC stands for body centered cubic.
To find out the edge length ‘a’, we should first see along which line the atoms are touching each other. In BCC it is the body diagonal, using pythagoras theorem we can see that body diagonal is (root.3 x a) which is equal to 4 times the radius of the atom (or 2 times diameter) along the same diagonal.
2d = 1.732 a ; a = 2 x 120 / 1.732 = 138.6 pm
