# Cahpter 23 Dual nature of radiation and matter¶

## Example 23.1 Page no 1200¶

In [10]:
#Given
h=6.62*10**-34                                     #J
c=3*10**8                                           #m/s
l=4.0*10**-7                                           #m

#Calculation
E=((h*c)/l)/1.6*10**-19
p=h/l

#Result
print"Value of energy is", round(E*10**38,1),"ev"
print"Momentum of photon is",p,"kg m/s"
Value of energy is 3.1 ev
Momentum of photon is 1.655e-27 kg m/s

## Example 23.2 Page no 1200¶

In [31]:
#Given
E=75*1.6*10**-19                           #J
h=6.62*10**-34                             #J s

#Calculation
f=E/h
l=(12400/E)*1.6*10**-19
f=c/(l*10**10)

#Result
print"Frequency of the photon is", round(f*10**5,0)*10**15,"Hz"
Frequency of the photon is 1.8e+16 Hz

## Example 23.3 Page no 1200¶

In [38]:
#Given
h=6.62*10**-34                           #Js
f=880*10**3                              #Hz
E1=10*10**3

#Calculation
E=h*f
n=E1/E

#Result
print"Number of photons emitted per second is", round(n*10**-31,3)*10**31
Number of photons emitted per second is 1.717e+31

## Example 23.4 Page no 1200¶

In [65]:
#Given
w=1.8
h=6.63*10**-34
l=5000*10**-10
m=9.0*10**-31

#Calculation
import math
W=12400/w
h1=(((h*c)/l)-(w*1.6*10**-19))
h2=h1/1.6*10**-19
vmax=math.sqrt((2*h1)/m)

#Result
print"(i) Threshold wavelength is",round(W,0),"A"
print"(ii) Maximum K.E of emitted photoelectrons is", round(h2*10**38,3),"ev"
print"(iii) Maximum velocity is",round(vmax*10**-5,0),"*10**5 m/s"
print"(iv) If the intensity of light is doubled, K.E of emitted electrons will remain unchanged"
(i) Threshold wavelength is 6889.0 A
(ii) Maximum K.E of emitted photoelectrons is 0.686 ev
(iii) Maximum velocity is 5.0 *10**5 m/s
(iv) If the intensity of light is doubled, K.E of emitted electrons will remain unchanged

## Example 23.5 Page no 1201¶

In [71]:
#Given
A=2*10**-4
I=30*10**-2
t=1
E=6.62*10**-19

#Calculation
n=(I*A)/E

#Result
print"Rate at which photons strike the surface is",round(n*10**-13,2)*10**13,"photons/s"
Rate at which photons strike the surface is 9.06e+13 photons/s

## Example 23.6 Page no 1201¶

In [100]:
#Given
h=6.62*10**-34                    #Js
c=3*10**8
l=4500*10**-10                     #m
w=2.3

#Calculation
E=(h*c)/l
E1=(E/1.6*10**-19)*10**38
K=E1-w
f0=(w*1.6*10**-19)/h
p=h/l

#Result
print"(i) The energy of photon is", round(E1,1),"ev"
print"(ii) The maximum kinetic energy of emitted electrons is",round(K,1),"ev"
print"(iii) Threshold frequency for sodium is",round(f0*10**-14,1)*10**14,"Hz"
print"(iv) Momentum of a photon is",round(p*10**27,1)*10**-27,"Kg m/s"
(i) The energy of photon is 2.8 ev
(ii) The maximum kinetic energy of emitted electrons is 0.5 ev
(iii) Threshold frequency for sodium is 5.6e+14 Hz
(iv) Momentum of a photon is 1.5e-27 Kg m/s

## Example 23.7 Page no 1202¶

In [16]:
#Given
l=36.0*10**-8              #m
w0=2*1.6*10**-19             #J
h=6.62*10**-34               #Js
c=3*10**8
e=1.6*10**-19
m=9.0*10**-31

#Calculation
import math
l0=(h*c)/w0
E=(h*c)/l
E1=(E/1.6*10**-19)*10**38
K=E1-2
v0=K
vmax=math.sqrt(e*v0*2/m)

#Result
print"(i) Threshold wavelength is",round(l0*10**10,0),"A"
print"(ii) Maximum kinetic energy of emitted photoelectrons is", round(K,3),"ev"
print"(iii) Stopping potential is",round(v0,3),"Volts"
print"(iv) Velocity is ",round(vmax*10**-5,2),"*10**5 m/s"
(i) Threshold wavelength is 6206.0 A
(ii) Maximum kinetic energy of emitted photoelectrons is 1.448 ev
(iii) Stopping potential is 1.448 Volts
(iv) Velocity is  7.18 *10**5 m/s

## Example 23.8 Page no 1202¶

In [13]:
#Given
h=6.62*10**-34
c=3*10**8
l0=24.8*10**-8
a=1.2
e=1.6*10**-19

#Calculation
w0=(h*c)/l0
w01=(w0/1.6*10**-19)*10**38
h1=w01+a
C=h1*e
l=(h*c)/C

#Result
print"Wavelength of incident light is", round(l*10**10,0),"A"
Wavelength of incident light is 2000.0 A

## Example 23.9 Page no 1203¶

In [15]:
#Given
v1=16.5
V0=6.6                   #V
f0=4.6*10**15                #Hz
f=2.2*10**15                  #Hz

#Calculation
h=(e*(v1-V0))/((f0-f))

#Result
print"Planck's constant is", h
Planck's constant is 6.6e-34

## Example 23.10 Page no 1203¶

In [9]:
#Given
h=6.62*10**-34
f0=44*10**13                     #Hz
a=11.5*10**14
b=4.4*10**14
e=1.6*10**-19

#Calculation
w0=((h*f0)/1.6*10**-19)*10**38
h=3/(a-b)
h1=h*e

#Result
print"(i) Work function of the material is", round(w0,2),"ev"
print"(ii) Plank's constant is", round(h1*10**34,2)*10**-34
(i) Work function of the material is 1.82 ev
(ii) Plank's constant is 6.76e-34

## Example 23.11 Page no 1204¶

In [18]:
#Given
h=6.6*10**-34
c=3*10**8
l=2000*10**-10
w0=4.2*1.6*10**-19
e=1.6*10**-19

#Calculation
K=((h*c)/l)-w0
v0=K/e
l1=(h*c)/w0

#Result
print"(i) Potential difference is", v0,"V"
print"(ii) Wavelength of incident light is", round(l1*10**10,0),"A"
(i) Potential difference is 1.9875 V
(ii) Wavelength of incident light is 2946.0 A

## Example 23.12 Page no 1204¶

In [33]:
#Given
h=6.6*10**-34
c=3*10**8
w0=2.39*1.6*10**-19
f1=4000.0                      #A
f2=6000                      #A
m=9.1*10**-31
e=1.9*10**-19
d=0.1

#Calculation
import math
l=(h*c)/w0
K=(12400/f1)-2.39
vmax=math.sqrt((2*K*1.6*10**-19)/m)
B=(m*vmax)/(e*d)

#Result
print"Maximum value of B is", round(B*10**5,2)*10**-5,"T"
Maximum value of B is 2.39e-05 T

## Example 23.13 Page no 1204¶

In [39]:
#Given
w0=4.4

#Calculation
l=12400/w0

#Result
print"Wavelength of visible light is", round(l,0),"A"
Wavelength of visible light is 2818.0 A

## Example 23.14 Page no 1205¶

In [45]:
#Given
h=6.625*10**-34
c=3*10**8
l=5600*10**-10
a=5

#Calculation
E=(h*c)/l
n=a/E

#Result
print"Number of visible photons emitted per second is", round(n*10**-19,2)*10**19
Number of visible photons emitted per second is 1.41e+19

## Example 23.15 Page no 1211¶

In [49]:
#Given
v=100

#Calculation
import math
l=12.27/math.sqrt(v)

#Result
print"Wavelength of an electron is", l,"A"
Wavelength of an electron is 1.227 A

## Example 23.16 Page no 1212¶

In [62]:
#Given
h=6.62*10**-34
m=9*10**-31
v=10**5
mp=1.67*10**-27

#Calculation
l=h/(m*v)
lp=h/(mp*v)

#Result
print"De-Broglie wavelength of electrons is", round(l*10**10,1)*10**-10,"m"
print"De-Broglie wavelength of protons is",round(lp*10**10,4)*10**-10 ,"m"
De-Broglie wavelength of electrons is 7.36e-09 m
De-Broglie wavelength of protons is 3.96e-12 m

## Example 23.17 Page no 1212¶

In [68]:
#Given
E=500*1.6*10**-19
mp=1.67*10**-27

#Calculation
import math
l=h/(math.sqrt(2*mp*E))

#Result
print"De-Broglie wavelength is", round(l*10**12,2)*10**-12,"m"
De-Broglie wavelength is 1.28e-12 m

## Example 23.18 Page no 1212¶

In [78]:
#Given
v=150.0
mn=1.675*10**-27                     #Kg
En=150*1.6*10**-19

#Calculation
import math
le=12.27/math.sqrt(v)
ln=h/math.sqrt(2*mn*En)

#Result
print"(i) De-Broglie wavelength of electron is",round(le,0),"A"
print"(ii) De-Broglie wavelength of neutron is", round(ln*10**10,4),"A"
(i) De-Broglie wavelength of electron is 1.0 A
(ii) De-Broglie wavelength of neutron is 0.0233 A

## Example 23.19 Page no 1213¶

In [81]:
#Given
l=2.0*10**-10                   #m
h=6.62*10**-34

#Calculation
p=h/l

#Result
print"Momentum of electrons is", p,"Kg m/s"
Momentum of electrons is 3.31e-24 Kg m/s

## Example 23.20 Page no 1213¶

In [87]:
#Given
l=1.4*10**-10                #m
h=6.63*10**-34
l1=2.0*10**-10

#Calculation
E=h*c*(1/l-1/l1)

#Result
print"Energy of the scattered electron is", round(E*10**16,2)*10**-16,"J"
Energy of the scattered electron is 4.26e-16 J

## Example 23.22 Page no 1213¶

In [95]:
#Given
me=9.11*10**-31                     #Kg
lp=1.813*10**-4
vp=3

#Calculation
mp=me/(lp*vp)

#Result
print"The particle's mass is", round(mp*10**27,3)*10**-27,"Kg. The particle is proton"
The particle's mass is 1.675e-27 Kg. The particle is proton

## Example 23.23 Page no 1214¶

In [103]:
#Given
l=0.82*10**-10                    #m
h=6.6*10**-34
m=9.1*10**-31

#Calculation
import math
le=math.sqrt((h*l)/(2*c*m))

#Result
print"Wavelength associated with the photoelectrons is", round(le*10**10,4),"A"
Wavelength associated with the photoelectrons is 0.0996 A