Question

Aluminum metal has 3 valence electrons per atom an atomic weight of 0.02698 kg/mole a density of 2700 \[kg/{{m}^{3}}\]and a conductivity of \[3.54\times {{10}^{7}}\] at the room temperature. now choose the correct option
(A) Number of free electrons increase with the increase in temperature
(B) Electron mobility for a sample at room temperature is \[3.6\times {{10}^{-3}}\]
(C) Electron mobility for a sample increase with temperature
(D) Electron mobility for a sample decreases with temperature

Answer 1

Hint: Aluminium is a metal whose atomic number is 13 and atomic weight is 27 u. It is a good conductor of heat and electricity. It has three electrons in its outermost shell and behaves as a good electron donor.

Complete step by step answer:
-Let us examine all the options one by one. The first statement says several free electrons increase with increase in temperature, free electrons are the electrons which are present in the outermost shell. The number is fixed and so their number does not increase with the increase in temperature.
-The second statement says electron mobility for a sample at room temperature is \[3.6\times {{10}^{-3}}\]. Quick looking at the physics book reveals that this is incorrect. Next option says electron mobility for a sample increases with temperature. Mobility is a proportionality constant between drift velocity and electric field. Increase in temperature decreases the relaxation time which in turn increases the mobility.

Hence, option (C) is correct.

Note: The ionic contribution to the total conductivity increases with increase in temperature. The electron mobility for Aluminium is \[3.8\times {{10}^{7}}{{\Omega }^{-1}}{{m}^{-1}}\]. Aluminium is one of the best conductors of electricity but it has a low melting point and thus at high voltage aluminum melts and catches fire easily.