In the classic model for electrical conduction, electron mobility u in a metal wire is defined as where v, is the drift velocity of the electrons and E is the electric field in the metal. This parameter is a measure of how freely electrons can travel through a metal when an electric field is applied, such as when the ends of a metal wire are connected to a potential difference. (a) Show that ng where a is the conductivity of the metal, n is the number density of the charge carriers, and q is the charge on each carrier. (Submit a file with a maximum size of 1 MB.) Choose Fle no file selected This answer has not been graded yet.

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In the classic model for electrical conduction, electron mobility u in a metal wire is defined as
where v, is the drift velocity of the electrons and E is the electric field in the metal. This parameter is a measure of how freely
electrons can travel through a metal when an electric field is applied, such as when the ends of a metal wire are connected to a
potential difference.
(a) Show that
where a is the conductivity of the metal, n is the number density of the charge carriers, and q is the charge on each carrier.
(Submit a file with a maximum size of 1 MB.)
Choose File no file selected
This answer has not been graded yet.
(b) B = AVH is often written as
AVH - R
IB
where R, is the Hall coefficient of the metal. Show that the following is true. (Submit a file with a maximum size of 1 MB.)
Hyo -n
(Choose File no file selected
This answer has not been graded yet
(c) The table below shows some measured values of Hall coefficients for some elemental materials. What is an average number
density (in m-3) of electrons in the first four elements?
Element
RH (10-11 m/(A )
Ag
-8.0
Al
-3.5
Au
-7.2
Cu
-5.5
Fe
+11
Sb
+200
0.11364E3 X
Take the average of the first four values in the table, and use the relationship between q, n, and R to solve for a typical n.
Note the Ry values given in the table should be multiplied by 10-11 (see the column header). m-3
(d) What do you think might be going on with the last two elements in the table in part (c)? Offer an explanation for why these
numbers differ so much from the first four elements in the table.
This answer has not been graded yet.
Transcribed Image Text:In the classic model for electrical conduction, electron mobility u in a metal wire is defined as where v, is the drift velocity of the electrons and E is the electric field in the metal. This parameter is a measure of how freely electrons can travel through a metal when an electric field is applied, such as when the ends of a metal wire are connected to a potential difference. (a) Show that where a is the conductivity of the metal, n is the number density of the charge carriers, and q is the charge on each carrier. (Submit a file with a maximum size of 1 MB.) Choose File no file selected This answer has not been graded yet. (b) B = AVH is often written as AVH - R IB where R, is the Hall coefficient of the metal. Show that the following is true. (Submit a file with a maximum size of 1 MB.) Hyo -n (Choose File no file selected This answer has not been graded yet (c) The table below shows some measured values of Hall coefficients for some elemental materials. What is an average number density (in m-3) of electrons in the first four elements? Element RH (10-11 m/(A ) Ag -8.0 Al -3.5 Au -7.2 Cu -5.5 Fe +11 Sb +200 0.11364E3 X Take the average of the first four values in the table, and use the relationship between q, n, and R to solve for a typical n. Note the Ry values given in the table should be multiplied by 10-11 (see the column header). m-3 (d) What do you think might be going on with the last two elements in the table in part (c)? Offer an explanation for why these numbers differ so much from the first four elements in the table. This answer has not been graded yet.
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