Comparison of Electrical Properties: Carbon vs Silicon
Carbon:
In diamond (a form of carbon), the atoms are bonded in a three
-dimensional tetrahedral lattice where each carbon atom forms four strong covalent bonds. This stable structure results in a large band gap between the valence band and the conduction band. Because the band gap is so wide, electrons cannot easily move to the conduction band, making diamond an insulator.
Silicon:
Silicon also forms a similar tetrahedral covalent lattice. However, it has a smaller band gap compared to diamond. At room temperature, some electrons in silicon can acquire enough thermal energy to jump from the valence band to the conduction band. This makes silicon a semiconductor, capable of conducting electricity under suitable conditions.
Conclusion:
The key difference in electrical properties arises from the band gap size:
Match the LIST-I with LIST-II
| LIST-I | LIST-II |
|---|---|
| A. Mobility of electrons (\(\mu\)) | I. \( Ne^2\tau/m \) |
| B. Drift velocity of electrons (\(v_d\)) | II. \( \mu E \) |
| C. Electrical conductivity of conduction electrons (\(\sigma\)) | III. \( \mu m/e \) |
| D. Relaxation time of electrons (\(\tau\)) | IV. \( 1/\rho ne \) |
Choose the correct answer from the options given below:
A racing track is built around an elliptical ground whose equation is given by \[ 9x^2 + 16y^2 = 144 \] The width of the track is \(3\) m as shown. Based on the given information answer the following: 
(i) Express \(y\) as a function of \(x\) from the given equation of ellipse.
(ii) Integrate the function obtained in (i) with respect to \(x\).
(iii)(a) Find the area of the region enclosed within the elliptical ground excluding the track using integration.
OR
(iii)(b) Write the coordinates of the points \(P\) and \(Q\) where the outer edge of the track cuts \(x\)-axis and \(y\)-axis in first quadrant and find the area of triangle formed by points \(P,O,Q\).