1. Give the significance of lattice point.
2. Explain how much portion of an atom located at (i) corner and (ii) body-centre of a cubic unit cell is part of its neighbouring unit cell.
3. A compound formed by elements A and B crystallises in the cubic structure, where A atoms are at the corners of a cube and B atoms are at the face centre. What is the formula of this compound ?
4. Atoms of element B forms hcp lattice and those of element A occupy 2/3rd of tetrahedral voids. What is the formula of compound formed by these elements A and B ?
5. The length of the unit cell of body centred metal crystal is 352 pm. Calculate the radius of an atom of the metal.
6. An element crystallises in bcc structure. The edge length of its unit cell is 288 pm. If the density of crystal is 7.2 gram per centimeter cube, what is the atomic mass of the element ?
7. Why is the coordination number 12 not found in ionic crystal ?
8. What is the value of radius ratio for
(i) tetrahedral void
(ii) octahedral void
9. Ionic solids, which have anionic vacancies due to metal excess defect, develop colour. Explain with the help of a suitable example.
10. The electrical conductivity of a metal decreases with rise in temperature while that of a semiconductor increases. Explain.
Solutions :-
Ans1. Significance of lattice point are:-
i) Lattice point in crystal lattice gives the location of one particle in space.
ii) Lattice point help to predict the geometry of lattice.
Ans2. In cubic unit cell, each corner is shared by eight unit cells and hence each atom is located at the corners of a cubic unit cell contributes 1/8th to the neighbouring unit cell. And for an atom present in body-centre is not shared by any other unit cell so it does not contribute to any of the neighbouring unit cell.
Ans3. 'A' atoms are at the 8 corners , each shared by 8 cubes, therefore, the number of A atom is = 8×1/8 = 1. B atoms are at the centres of 6 faces and each atom at the face can be shared by two cubes, therefore, the number of B atoms =6×1/2 = 3. Thus, the formula of compound is AB3.
Ans4:- Since the number of tetrahedral voids formed is double the number of atoms of element B and atoms of A occupy only 2/3rd of tetrahedral voids, therefore only 2/3rd of these are occupied by the atoms of element A. Thus, the ratio of the number of atoms of A and B is 2×2/3 : 1 or 4:3 and the formula of the compound would be A4B3.
Ans5:- For bcc, a=4r/√3
Or, r=a√3/4 = 352×1.733/4
So, r= 152.4 pm
Ans6:- a=288pm
d= 7.2 gram per centimeter cube
Z=2
NA = 6.023×10²³
M = ?
Wo know that,
d = Z×M/a³×NA
M= d×a³×NA/Z
M=7.2 ×(288)³ × 6.023 × 10²³/2 × 10³0
M = 51.8u
So atomic mass of the element = 51.8 u
Ans7:- The coordination number greater than 8 is not possible since the radius ratio in the range 0.732 to 1.0 forms a cubic void, the geometrical shape with maximum coordination number.
Ans8:- i) For Tetrahedral void, radius ratio is 0.225
ii) For octahedral void, the radius ratio is 0.414.
Ans9:- Alkali metal halides such as NaCl, KCl and LiCl shows metal excess defect due to anionic vacancies.
For example, when crystal of NaCl are heated in atmosphere of sodium vapours, sodium atoms get deposited on the surface of the crystal. The chlorine negative ions from the crystal lattice diffuse to the surface of the crystal and combines with Na atoms to give NaCl. Sodium atoms due to it's low ionization enthalpy loses an electron to form sodium positive ion. The released electron diffused into the crystal and occupy anionic sites. The anionic sites occupied by unpaired electron is called F-centre. They impart yellow color to the NaCl crystal. The color imparted is due to the excitation of these electrons when they absorb energy from the visible light, falling on the crystal. Similarily, excess of potassium makes KCl crystal Violet and excess of lithium makes LiCl crystal pink.
Ans10:- The electrical conductivity of a metal decreases with increase in temperature because vibration of kernels increase which cause hindrance in the flow of electrons. In case of semiconductors, the conductivity is due to the presence of impurities and defects in material of the semiconductor. With the increase in temperature, there is increase in the number of defects and thus there is increase in the electrical conductivity.