# Chapter 4 Wave nature of matter and the need for a wave function¶

## Example 4.1 Page no 58¶

In [5]:
#Given
V=100                                     #volts

#Calculation
import math
wavelength=12.3/(math.sqrt(V))

#Result
print"de Broglie wavelength of electrons ", wavelength,"A"

de Broglie wavelength of electrons  1.23 A


## Example 4.2 Page no 58¶

In [109]:
#Given
K=100                                       #ev
h=6.63*10**-34
m=9.1*10**-31
e=1.6*10**-19

#Calculation
import math
v=h/(math.sqrt(2*m*K*e))

#Result
print"de broglie wavelength of electrons ",round(v*10**10,1),"A"

de broglie wavelength of electrons  1.2 A


## Example 4.3 Page no 58¶

In [113]:
#Given
m=1.675*10**-27                                 #mass of neutron in kg
v=1.4*10**-10                                   #de broglie wavelength in m
h=6.63*10**-34                                  #Js

#Calculation
K=(h**2/(2*m*(v**2)))/(1.6*10**-19)

#Result
print"Kinetic energy of neutron is ", round(K*10**2,2),"*10**-2 ev"

Kinetic energy of neutron is  4.18 *10**-2 ev


## Example 4.4 Page no 58¶

In [64]:
#Given
E=-3.4                                        #total energy in ev
h=6.63*10**-34                                #Js
m=9.1*10**-31
e=1.6*10**-19

#Calculation
import math
K=-E
v=h/(math.sqrt(2*m*K*e))

#Result
print"(a) Kinetic energy ",K,"ev"
print"(b) de broglie wavelength of the electron is ",round(v*10**10,3),"A"

(a) Kinetic energy  3.4 ev
(b) de broglie wavelength of the electron is  6.663 A


## Example 4.5 Page no 59¶

In [116]:
#Given
m=1.672*10**-27                         #mass of neutron in kg
h=6.60*10**-34                          #Js
v=1.0*10**-10                           #de broglie wavelength in m

#Calculation
K=(h**2/(2.0*m*v**2))/(1.6*10**-19)

#Result
print"Kinetic energy of a neutron is ", round(K*10**2,2),"*10**-2 ev"

Kinetic energy of a neutron is  8.14 *10**-2 ev


## Example 4.6 Page no 59¶

In [87]:
#Given
m=10*10**-3                                        #mass of a ball in kg
v=1                                                #Speed in m/s
h=6.63*10**-34                                     #Js

#Calculation
V=h/(m*v)                                          #Wavelength

#Result
print "de broglie wavelength is ",V,"m"
print"This wavelength is negligible compared to the dimensions of the ball. therefore its effect can not be observed."

de broglie wavelength is  6.63e-32 m
This wavelength is negligible compared to the dimensions of the ball. therefore its effect can not be observed.


## Example 4.7 Page no 59¶

In [94]:
#Given
T=27                            #temperature in degree c
K=1.38*10**-23                  #boltzmann constant in J/K
h=6.63*10**-34                  #Js
m=1.67*10**-27

#Calculation
import math
T1=T+273
v=h/(math.sqrt(2*m*K*T1))

#Result
print"de broglie wavelength is ",round(v*10**10,2),"A"

de broglie wavelength is  1.78 A


## Example 4.10 Page no 64¶

In [117]:
#Given
V=100                                    #ev
a=10                                     #degree
n=1

#Calculation
import math
v=12.3/(math.sqrt(V))                   #De broglie wavelength
d=v/(2*math.sin(a*3.14/180.0))
n=(2*d)/v

#Result
print"(a) Spacing between the crystal plane is ", round(d,2),"A"
print"(b) Peaks in the interference pattern is ",round(n,2)
print"the largest possible value of n is 5"

(a) Spacing between the crystal plane is  3.54 A
(b) Peaks in the interference pattern is  5.76
the largest possible value of n is 5