14: Waves and Particles

Example number 14.1, Page number 17

In [3]:
#importing modules
import math
from __future__ import division

#Variable declaration
V=150;    #potential difference(V)
e=1.6*10**-19;   #charge of electron(c)
m=9.1*10**-31;   #mass of electron(kg)
h=6.626*10**-34;   #planck's constant

#Calculation
lamda=h/math.sqrt(2*m*e*V);    #de broglie wavelength of electron(m)

#Result
print "de broglie wavelength of electron is",round(lamda*10**10,5),"*10**-10 m"

de broglie wavelength of electron is 1.00256 *10**-10 m

Example number 14.2, Page number 17

In [6]:
#importing modules
import math
from __future__ import division

#Variable declaration
E=0.025;    #energy of electron(MeV)
e=1.6*10**-19;   #charge of electron(c)
m=9.1*10**-31;   #mass of electron(kg)
h=6.626*10**-34;   #planck's constant

#Calculation
E=E*10**6*e;   #energy of electron(J)
v=math.sqrt(2*E/m);   #velocity of electron(m/s)
lamda=h/(m*v);    #de broglie wavelength(m)

#Result
print "de broglie wavelength is",round(lamda*10**10,5),"angstrom"

de broglie wavelength is 0.07766 angstrom

Example number 14.3, Page number 18

In [9]:
#importing modules
import math
from __future__ import division

#Variable declaration
E=1;    #kinetic energy of electron(MeV)
e=1.6*10**-19;   #charge of electron(c)
m=9.1*10**-31;   #mass of electron(kg)
h=6.626*10**-34;   #planck's constant

#Calculation
E=E*10**6*e;   #energy of electron(J)
v=math.sqrt(2*E/m);   #velocity of electron(m/s)
lamda=h/(m*v);    #de broglie wavelength of electron(m)

#Result
print "de broglie wavelength of electron is",round(lamda*10**10,5),"angstrom"

de broglie wavelength of electron is 0.01228 angstrom

Example number 14.4, Page number 18

In [17]:
#importing modules
import math
from __future__ import division

#Variable declaration
V=100;    #potential difference(V)
e=1.6*10**-19;   #charge of electron(c)
m=9.1*10**-31;   #mass of electron(kg)
h=6.626*10**-34;   #planck's constant
c=3*10**8;    #velocity of light(m/s)

#Calculation
v=math.sqrt(2*e*V/m);   #velocity of electron(m/s)
u=c**2/v;     #phase velocity of electron(m/s)
lamda=h/(m*v);    #de broglie wavelength of electron(m)
p=m*v;    #momentum of electron(kg m/s)
vbar=1/lamda;   #wave number of electron wave(per m)

#Result
print "velocity of electron is",round(v/10**6,5),"*10**6 m/s"
print "phase velocity of electron is",round(u/10**10,4),"*10**10 m/s"
print "de broglie wavelength of electron is",round(lamda*10**10,3),"angstrom"
print "momentum of electron is",round(p*10**24,3),"*10**-24 kg m/s"
print "wave number of electron wave is",round(vbar/10**9,3),"*10**9 per m"

velocity of electron is 5.92999 *10**6 m/s
phase velocity of electron is 1.5177 *10**10 m/s
de broglie wavelength of electron is 1.228 angstrom
momentum of electron is 5.396 *10**-24 kg m/s
wave number of electron wave is 8.144 *10**9 per m

Example number 14.5, Page number 19

In [19]:
#importing modules
import math
from __future__ import division

#Variable declaration
deltax=10**-14;   #radius of nucleus(m)
m=1.67*10**-27;   #mass of proton(kg)
h=6.626*10**-34;   #planck's constant
e=1.6*10**-19;   #charge of electron(c)

#Calculation
deltap=h/(2*math.pi*deltax);   #uncertainity in momentum of proton(kg m/s)
KE=deltap**2/(2*m);    #minimum kinetic energy of proton(J)
KE=KE/(e*10**6);    #minimum kinetic energy of proton(MeV)

#Result
print "uncertainity in momentum of proton is",round(deltap*10**20,4),"*10**-20 kg m/s"
print "minimum kinetic energy of proton is",round(KE,3),"MeV"

uncertainity in momentum of proton is 1.0546 *10**-20 kg m/s
minimum kinetic energy of proton is 0.208 MeV

Example number 14.6, Page number 20

In [21]:
#importing modules
import math
from __future__ import division

#Variable declaration
deltax=0.1*10**-10;   #uncertainity in position of electron(m)
h=6.626*10**-34;   #planck's constant

#Calculation
deltap=h/(2*math.pi*deltax);   #uncertainity in momentum of electron(kg m/s)

#Result
print "uncertainity in momentum of electron is",round(deltap*10**23,4),"*10**-23 kg m/s"

uncertainity in momentum of electron is 1.0546 *10**-23 kg m/s

Example number 14.7, Page number 20

In [30]:
#importing modules
import math
from __future__ import division

#Variable declaration
m=9.1*10**-31;   #mass of electron(kg)
h=6.626*10**-34;   #planck's constant
a=1*10**-10;   #width of potential wall(m)
n1=1; 
n2=2;
n3=3;
e=6.24*10**18;  #conversion factor from J to eV

#Calculation
En=(h**2)/(8*m*(a**2));   #energy of electron(J)
E1=En*n1**2;   #energy of 1st excited state(J)
E1=E1*e;   #energy of 1st excited state(eV)
E2=En*n2**2;   #energy of 2nd excited state(J)
E2=E2*e;   #energy of 2nd excited state(eV)
E3=En*n3**2;   #energy of 3rd excited state(J)
E3=E3*e;   #energy of 3rd excited state(eV)

#Result
print "first 3 permitted energy levels of electron are",round(E1,2),"eV",round(E2,2),"eV and",round(E3,2),"eV"
print "answers given in the book vary due to rounding off errors"

first 3 permitted energy levels of electron are 37.63 eV 150.53 eV and 338.69 eV
answers given in the book vary due to rounding off errors