#importing module
import math
from __future__ import division
#Variable declaration
k=1.376*10**-23 #Boltzmann's constant in J/K
T=300 #Temperature
m=9.11*10**-31 #Mass of electron
#Calculations
v=math.sqrt((3*k*T)/m)/10**5
#Result
print"root mean square velocity v= %1.2f*10**5 m/s" %v
#importing module
import math
from __future__ import division
#Variable declaration
sigma=6.8*10**7 #conductivity
n=8.5*10**28 #number of electrons
m=9.1*10**-31 #Mass of electron
e=1.6*10**-19 #charge on electron
k=1.38*10**-23 #Boltzmann's constant in J/K
T=300 #temperature in K
#Calculations
lamda=(2*sigma*math.sqrt(3*m*k*T))/(n*e**2)/10**-9
#Result
print"Mean free path for electron= %1.1f*10**-9 m" %lamda
#importing module
import math
from __future__ import division
#Variable declaration
rho=1.54*10**-8 #resistivity
n=5.8*10**28 #electron density
e=1.602*10**-19 #charge on electron
m=9.1*10**-31 #Mass of electron
#Calculations
tau=m/(n*(e**2)*rho)/10**-14
#Result
print"Relaxation time= %1.2f*10**-14 seconds" %tau
#importing module
import math
from __future__ import division
#Variable declaration
EF=1.1214*10**-18 #fermi energy in J
m=9.11*10**-31 #Mass of electron
h=6.63*10**-34 #planck's constant
#Calculations
n=((8*m*EF)/(h**2))**(3/2)*(math.pi/3)/10**28
#Result
print"No. of free electrons per unit volume= %1.3f*10**28 electrons per meter**3" %n
#importing module
import math
import numpy as np
from __future__ import division
#Variable declaration
fE=0.01 #probability
delE=8*10**-20 #ev to J
#Calculations
T=5797/np.log(99)
#Result
print"Temperature= %i" %T,"K"