Arrange the mobilities of the following in descending order :
A. electrons in a semiconductor
B. ions in an electrolyte solution
C. proton \( (\mathrm{H^{+}}) \) in an electrolyte solution
D. holes in a semiconductor
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → A, D, C, B
Mobility is the drift speed per unit field, \( \mu = v_d/E = e\tau/m \). Light carriers moving through a crystal have mobilities many orders of magnitude larger than ions that must push their way through a liquid.
Typical values at room temperature (silicon; ions in water):
\( \text{(A) electrons in a semiconductor (Si): } \mu \approx 0.14\,\mathrm{m^{2}\,V^{-1}\,s^{-1}} \)
\( \text{(D) holes in a semiconductor (Si): } \mu \approx 0.05\,\mathrm{m^{2}\,V^{-1}\,s^{-1}} \)
\( \text{(C) proton } (\mathrm{H^{+}}) \text{ in an electrolyte solution (water): } \mu \approx 3.6\times10^{-7}\,\mathrm{m^{2}\,V^{-1}\,s^{-1}} \)
\( \text{(B) ions in an electrolyte solution (e.g. } \mathrm{Na^{+}, Cl^{-}}\text{): } \mu \approx 5\text{ to }8\times10^{-8}\,\mathrm{m^{2}\,V^{-1}\,s^{-1}} \)
Holes move by bound electrons jumping from bond to bond, which is slower than the motion of free conduction electrons. A proton in water is handed on from one water molecule to the next along hydrogen bonds instead of dragging itself through the liquid, so it is several times more mobile than any other ion.
\( \mu_A \gt \mu_D \gt \mu_C \gt \mu_B \)
The order is A, D, C, B.