Chapter05:Electron Theory of Metals

Ex5.1.i:pg-110

In [8]:
# Example 5.1.i: probability for diamond
 
# given :

Eg=5.6; # in eV
k=86.2*10**-6; # in eVk**-1
T=273+25.0; # in K
E_Ef=Eg/2;
f_E=1/(1+math.exp(E_Ef/(k*T)));
print "{:.2e}".format(f_E)," is probability for diamond"

4.58e-48  is probability for diamond

Ex5.1.ii:pg-110

In [10]:
# Example 5.1.ii: probability for silicon
 
# given :
Eg=1.07; # in eV
k=86.2*10**-6; # in eVk**-1
T=273+25.0; # in K
E_Ef=Eg/2;
f_E=1/(1+math.exp(E_Ef/(k*T)));
print "{:.2e}".format(f_E),"is probability for diamond "
# answer is wrong in book

9.01e-10 is probability for diamond

Ex5.2:pg-119

In [14]:
# Example 5.2: resistance
 
# given :
l=1; # length in m
A=4*10**-4; # area of cross section in m**2
p=0.01*10**-2; # resistivity in ohm-m
R=p*(l/A);
print R,"is resistance of wire,R(ohm) "

0.25 is resistance of wire,R(ohm)

Ex5.3:pg-120

In [16]:
# Example 5.3: resistance
 
# given :

p=1.7*10**-8; #  resistivity i ohm-m
d=0.0005; # diameter of the wire in m
l=31.4; # length in m
A=(math.pi*d**2)/4;
R=p*(l/A);
print round(R,2),"is resistance of wire,R(ohm) "

2.72 is resistance of wire,R(ohm)

Ex5.4:pg-120

In [11]:
# Example 5.4: conductivity
 
# given :

V=.432; # voltage drop across the wire in volts
I=10; # current through the wire in A
l=1; # length in m
d=1*10**-3; # diameter in m
R=V/I;
A=(math.pi*d**2)/4;
p=(R*A)/l;
b=1/p;
print "{:.2e}".format(b)," is conductivitty,b(ohm**-1.m**-1) "

2.95e+07  is conductivitty,b(ohm**-1.m**-1)

Ex5.5:pg-124

In [20]:
# Example 5.5: drift velocity
 
# given :

n=10**19; # in m**3
b=0.01; # conductivity in ohm**-1. m**-1
V=0.17; # in volts
d=.27*10**-3; # in m
e=1.602*10**-19; # in C
m=9.1*10**-31; # in kg
E=V/d; # in volt/m
v=((b*E)/(n*e));
print round(v,2),"is drift velocity of electron,v (m/sec) "

3.93 is drift velocity of electron,v (m/sec)

Ex5.6:pg-124

In [15]:
# Example 5.6: conductivity
 
# given :
e=1.6*10**-19; # in C
T=300; # temerature in K
t=2*10**-14; # time in sec
c=63.54; # atomic weight of copper in a.m.u
m=9.1*10**-31; # mass in kg
# we know that 63.45 grams of copper contains 6.023*10**23 free electrons since one atom contributes one electron.the volume of 63.54 gram of copper is 8.9 cubic centimetre(c.c).
n=6.023*10**23/(c/8.9); #number of electrons per unit volume(c.c)
n1=n*10**6; # the number of electrons per m**3
b=(e**2*n1*t)/m;
print "{:.2e}".format(b),"is conductivity,b(mho/m) "

4.75e+07 is conductivity,b(mho/m)

Ex5.7:pg-125

In [16]:
# Example 5.7: mobility of electrons
 
# given :

e=1.602*10**-19; # in C
m=9.1*10**-31; # in kg
t=10**-14; # time in sec
mu=(e*t)/m;
print "{:.2e}".format(mu),"is mobility of electrons,mu(m**2/volts.sec) "

1.76e-03 is mobility of electrons,mu(m**2/volts.sec)

Ex5.8:pg-125

In [27]:
# Example 5.8: mobility 
 
# given :

d=10.5; # density of silver in gm/c.c
w=107.9; # atomic weight
b=6.8*10**5; # conductivity in mhos/cm
e=1.602*10**-19; # in C
N=6.023*10**23;
n=(N*d)/w;
mu=b/(e*n);
print round(mu,2),"is mobility of electron,mu(m**2/volt-sec) "

72.42 is mobility of electron,mu(m**2/volt-sec)

Ex5.9:pg-126

In [18]:
# Example 5.9: mobility and drift velocity
 
# given :
b=6.5*10**7; # conductivity in ohm**-1.m**-1
e=1.602*10**-19; # in C
n=6*10**23; #
E=1; # in V/m
mu=b/(e*n);
v=mu*E;
print "{:.2e}".format(mu),"is mobility ,mu(m**2/volt-sec) "
print "{:.2e}".format(v),"is drift velocity,v(m/sec) "
# mobility and drift is calculated wrong in book

6.76e+02 is mobility ,mu(m**2/volt-sec) 
6.76e+02 is drift velocity,v(m/sec)

Ex5.10:pg-126

In [24]:
#Example 5.10 : density and drift velocity 
 
#given data :

e=1.602 *10**-19;
b=58*10**6;# in ohm**-1 m**-1
mu_n=3.5*10**-3;# in m**2/V s
E=0.5; # in V/m
n=b/(e*mu_n)
print "{:.2e}".format(n),"is density,n(m**-3) "
v=mu_n*E;
print "{:.2e}".format(v),"is drift velocity,v(m/s) "

1.03e+29 is density,n(m**-3) 
1.75e-03 is drift velocity,v(m/s)

Ex5.11:pg-127

In [26]:
#Example 5.11 : velocity
import math
#given data :
m=9.109*10**-31; # in kg
e=1.602 *10**-19;
Ef=2.1# in ev
Wf=e*Ef;# in J
vf=math.sqrt((2*Wf)/m);
print "{:.1e}".format(vf),"is velocity,vf(m/s) "

8.6e+05 is velocity,vf(m/s)

Ex5.12.a:pg-127

In [27]:
#Example 5.12.a : velocity
 
#given data :
m=9.1*10**-31; # in kg
e=1.602 *10**-19;
Ef=3.75;# in ev
Wf=(e*Ef);# in J
vf=math.sqrt(((2*Wf)/m));
print "{:.2e}".format(vf)," is velocity,vf(m/s) "
# answer is wrong in book

1.15e+06  is velocity,vf(m/s)

Ex5.12.b:pg-127

In [28]:
#Example 5.12.b : mobility of electron
 
#given data :
m=9.1*10**-31; # in kg
e=1.602 *10**-19;
Ef=3.75;# in ev
t=10**-14;# in sec
mu=(e*t)/m;
print "{:.2e}".format(mu),"is mobility,mu(m**2/V-sec) "

1.76e-03 is mobility,mu(m**2/V-sec)

Ex5.13:pg-127

In [39]:
#Example 5.13 : the mean free path
import math
#given data :

t=10**-9; # in sec
m=9.109*10**-31; # in kg
e=1.602 *10**-19;
Ef=7# in ev
Wf=e*Ef;# in J
vf=math.sqrt((2*Wf)/m);
lamda=vf*t*10**3;
print round(lamda,2),"is the mean free path,lamda(mm) "

1.57 is the mean free path,lamda(mm)

Ex5.14:pg-128

In [42]:
#Example 5.14 : mobility and average time
 
#given data :

m=9.109*10**-31; # in kg
e=1.602 *10**-19;
d=8.92*10**3;# in kg/m**3
p=1.73*10**-8;# ohm-m
A=63.5;#atomic weight
N=6.023*10**22; # avogadro's number
n=(N*d)/A;
b=1/p;# conductivity
mu=b/(n*e);
print round(mu,1),"= mobility,mu(m**2/V-s)  "
t=(mu*m)/e;
print round(t*10**9,3),"= average time,t(ns)  "

42.6 = mobility,mu(m**2/V-s)  
0.242 = average time,t(ns)

Ex5.15:pg-129

In [30]:
#Example 5.15 : electrical resistivity
import math
#given data :

r=1.86*10**-10;# in m
t=3*10**-14;# in sec
a=2;
m=9.1*10**-31; # in kg
e=1.602 *10**-9;
A=23*10**-3;#in kg/m
N=6.023*10**23; # avogadro's number
M=(a*A)/N;
V=((4/math.sqrt(3))*r)**3;
d=M/V;
mu=((e*t)/m);
n=(N*d)/A;
b=1.602 *10**-19*n*mu;
p=(1/b);
print "{:.1e}".format(p),"= resistivity,p(ohm-m) "

4.7e-18 = resistivity,p(ohm-m)