In a pure semiconductor, the number of free electrons is 6 x 1019/m3. The total number of electrons in the same semiconductor of size 1 cm x 1 cm x 2 mm is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 12 x 1012
The number of free electrons in a piece of semiconductor is the free-electron density multiplied by the volume of the piece, with every length in metres.
\( \displaystyle V = (1\times10^{-2}\,\mathrm{m}) \times (1\times10^{-2}\,\mathrm{m}) \times (2\times10^{-3}\,\mathrm{m}) \)
\( \displaystyle V = 2\times10^{-7}\,\mathrm{m^{3}} \)
\( \displaystyle N = nV = (6\times10^{19}\,\mathrm{m^{-3}}) \times (2\times10^{-7}\,\mathrm{m^{3}}) \)
\( \displaystyle N = 12\times10^{12} \)
Note: It seems that there is a mistake in the original NTA paper, which asks for “the total number of electrons” when it should read “the total number of free electrons”. A semiconductor also contains a very large number of bound electrons, which cannot be found from the data. The only density given is that of free electrons, so the intended meaning is clear and the question can still be solved.