The Solid State

Question 125
CBSEENCH12005473

If the radius of the octahedral void is r and radius of the atoms in close packing is R, derive relation between r and R.

Solution
An octahedral void is shown in Fig. Though an octahedral void is surrounded by six spheres, only four are shown. The spheres present above and below the void are not shown. Let us assume that the edge length of the unit cell is a cm and raius of octahedral void is r and the radius of sphere is R.


In the given figure, let an sphere having centre ‘O’ is fitted in the octahedral void.
As given, radius of the sphere fitted in the octahedral void = r

And radius of the atoms in close packing = R

Question 126
CBSEENCH12005474

Pure silicon is an insulator. Silicon doped with phosphorus is a semi-conductor. Silicon doped with gallium is also a semiconductor. What is the difference between the two doped silicon semi-conductor?

Solution

Phosphorus has one excess valence electron (compared with Si) after forming the four covalent bonds normally with silicon. This excess electron gives rise to electronic conduction. That is why silicon becomes semi-conductor on doping with phosphorus. It is called n-type semi-conductor.

Gallium has only three valence electrons. It creates an electron deficient bond or a hole when it is doped with silicon. Such holes can move in the crystal giving rise to electrical conductivity. Thus silicon doped with gallium is also semi-conductor due to movement of holes. It is called-p-type semiconductor.

Question 127
CBSEENCH12005475

What are paramagnetic and ferromagnetic substances. Account for the paramagnetic character of transition metal compounds. How does the paramagnetic character of the bivalent ions of the first transition metal series varies from Ti (Z = 22) to Cu (Z = 29)?

Solution

Paramagnetic substances are attracted by the magnetic field. This is due to the presence of unpaired electrons in the atoms/ions/molecules of the paramagnetic substance. Paramagnetism is a temporary effect.

Ferromagnetic substances are strongly attracted by the magnetic field. They show magnetism even when the magnetic field is removed. This is due to a spontaneous alignment of the magnetic dipole in the same direction.

Transition metal compounds contains one or more unpaired electrons. So, these compounds show para magnetism. The paramagnetism of the bivalent ions of the first transition metal series first increases in going from Ti2+ to Mn2+ (number of unpaired electrons increases) and then decreases upto Cu2+ (because the number of unpaired electrons decreases).
Transition metal compounds contains one or more unpaired electrons. So, these compounds show para magnetism. The paramagnetism of the bivalent ions of the first transition metal series first increases in going from Ti2+ to Mn2+ (number of unpaired electrons increases) and then decreases upto Cu2+ (because the number of unpaired electrons decreases).

Question 128
CBSEENCH12005476

Non-stoichiometric cuprous oxide, Cu2O can be prepared in laboratory. In this oxide, copper to oxygen ratio is slightly less than 2 :1. Can you account for the fact that this substance is a p-type semi-conductor ?

Solution

In the sample of cuprous oxide, Cu2O prepared in laboratory, copper to oxygen ratio is less than 2 : 1 and this deficiency of copper causes the metal deficiency defects.
In these defects the positive ions are less in number as compared to anions. These defects are caused in two ways:
(i) By Cation Vacancies : Some Cu+ may be missing from lattice sites and their positive charges are balanced by presence of extra charge on adjacent cations i.e., some Cu2+ are present and some cation vacancies are present.

(ii) By presence of extra anions at interstitial sites: The type of defect can arise where some oxide ion, O2– are present at lattice sites and their charge is balanced by neighbouring cations in higher oxidation states i.e., some Cu2+ ions are present instead of Cu2+ ions.

Metal deficiency defect due cation vacancy.

Metal deficiency defect due to presence of extra anions.

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