Solid State Physics-I

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Chapter#3: Cohesive Energy

Team Quanta presents all possible short questions of BS Physics book Solid State Physics – I’s Chapter#3: Cohesive Energy.

Q.1 All metals are opaque to light of all wavelengths and have high luster. Explain.

Answer: The opacity and luster of metals is due to presence of free electrons in metallic bonding. The electrons first absorb energy from and other electromagnetic radiation and then radiate the same producing lustrous appearance.

Q.2 Metal crystals share easily. Explain.

Answer: Metal crystals share easily as they are held together by a cloud of free electrons and not by covalent bonds. The energy of these electrons is affected remarkably by change in volume so that there is, in general good cleavage strength. The energy is affected by very little by the movement of atoms which does not change the volume making the metals malleable and ductile. Again metals have uniformly positive ions placed in uniform electron gas. Therefore, the displacement of ions produces the same environment. Hence metals can be easily formed that is they are malleable and ductile.

Q.3 What is cause of directional nature of covalent bonds?

Answer: In covalent bonds, shared electron pair is concentrated along the line joining the two atoms sharing the electrons. Therefore covalent bond is directional bond.

Q.4  State three important properties of metals.

Answer: Three important properties of metals are listed below:

  • Metals are opaque.
  • Metals are good conductors of heat and electricity.
  • Metals are malleable i.e. can be beaten into sheets and ductile i.e. can be drawn into wires.

Q.5. Write down expression for electrostatic energy of structure of 2N ions of charge ±q.

Answer: Lattice energy of crystal composed of 2N ions is given by,

    \[U=-N\alpha\left(\frac{q^2}{4\pi\epsilon_0r}\right)+Nz\lambda e^{-\frac{r}{\rho}}\]

At equilibrium separation,

    \[\left(\frac{dU}{dr}\right)_{r=r_0}=0\]

    \[\Rightarrow N\alpha\left(\frac{q^2}{4\pi\epsilon_0r_0^2}\right)+Nz\lambda e^{-\frac{r_0}{\rho}}\left(-\frac{1}{\rho}\right)=0\]

    \[\Rightarrow e^{-\frac{r}{\rho}}=\frac{q^2\alpha\rho}{4\pi\epsilon_0z\lambda r_0^2}\]

So,

    \[U=-N\alpha\left(\frac{q^2}{4\pi\epsilon_0r_0}\right)\left(1-\frac{\rho}{r_0}\right)\]

Which is required expression for electrostatic energy of structure of ions of charge  ±q.

Q.6 Show that 1eV per mole = 23kcal/mole .

Answer: We know that,

    \[1eV=1.6\times{10}^{-19}J\]

    \[\Rightarrow1eV\ per\ mol=1.6\times{10}^{-19}\times6.023\times{10}^{23}J\]

    \[\Rightarrow1eV\ per\ mol=\frac{9.635\times{10}^4}{4.184\times{10}^3}\ \frac{kcal}{mol=23.029kcal\approx23\frac{kcal}{mol}}\]

Q.7 Give Pauling formula for iconicity of covalent bond A-B.

Answer: Pauling in 1960 expressed iconicity of a covalent bind A-B in terms of difference between electro negativities of these two atoms:

    \[f_i=1-exp\left(\frac{\left(X_A-X_B\right)^2}{4}\right)\]

Here  is fractional ionic character of bond,  are Pauling electro negativities of elements A and B.

Q.8 Given a solid made up of molecules possessing permanent dipoles and another made up of molecules possessing only induced dipoles, which will show most dependent properties.

Answer: The solid containing permanent dipoles will be more affected by temperature than will the induced dipoles since degree of polarization is temperature dependent in former but not in the later.

Q.9 Define ionization energy and electron affinity.

Answer: Ionization energy is amount of energy required to remove an electron from an atom in ground state. Electron affinity is amount of energy released when a neutral atom gains an electron.

Q.10.What are different types of bonding between atoms? Give examples of each type.

Answer: Different types of bonding in crystals are:

  • Covalent bonding
  • Examples are silicon, germanium and diamond.
  • Ionic bond
  • Examples is
  • Hydrogen bonding
  • Example is ice.
  • Van der Waals bonding
  • Examples are Ne and Ar.
  • Metallic bonding
  • Examples are metals and alloys.

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