# Chapter 28 Particle nature of radiation¶

## Example 28.1 Page no 801¶

In [7]:
#Given
l=4950.0*10**-10
h=6.6*10**-34                             #js
c=3*10**8                                 #m/s

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

#Result
print"Energy of each photon is",E,"eV"

Energy of each photon is 2.5 eV


## Example 28.2 Page no 801¶

In [8]:
#Given
E=6.62                      #J
v=10**12                          #Hz
h=6.62*10**-34

#Calculation
E1=h*v
n=E/(h*v)

#Result
print"Number of photons is",n

Number of photons is 1e+22


## Example 28.3 Page no 801¶

In [38]:
#Given
h=6.62*10**-34                        #js
c=3*10**8                            #m/s
Iev=1.6*10**-19                      #J
V=10**6                               #hz
V1=5890*10**-10                       #m
L=10.0**-10                             #m

#Calculation
E=h*v
E1=E/Iev
A=(h*c)/V1
A1=A/Iev
B=(h*c)/L
B1=B/Iev

#Result
print"(i) The energy of a photon with frequency 1000 Khz is",round(E1*10**3,2),"10**-9","ev"
print"(ii) The energy of a photon when wavelength is 5890A is",round(A1,2) ,"eV"
print"(iii) The energy of a photon when wavelength is 1 A is", B1,"eV"

(i) The energy of a photon with frequency 1000 Khz is 4.14 10**-9 ev
(ii) The energy of a photon when wavelength is 5890A is 2.11 eV
(iii) The energy of a photon when wavelength is 1 A is 12412.5 eV


## Example 28.4 Page no 801¶

In [45]:
#Given
l=0.66*10**-10                     #m
h=6.62*10**-34                     #Js
c=3*10**8                            #m/s

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

#Result
print"(a) Maximum energy of photon is",round(E*10**-3,2),"Kev"
print"(b) To produce electrons of energy 18.81 Kev,accelerating potential of 18.81 KV"

(a) Maximum energy of photon is 18.81 Kev
(b) To produce electrons of energy 18.81 Kev,accelerating potential of 18.81 KV


## Example 28.5 Page no 801¶

In [60]:
#Given
E=10.2*10**9                         #ev
h=6.62*10**-34
c=3*10**8

#Calculation
E1=(E/2.0)*(1.6*10**-19)
l=(h*c)/E1

#Result
print"Wavelength is",round(l*10**16,3),"10**-16"

Wavelength is 2.434 10**-16


## Example 28.6 Page no 802¶

In [75]:
#Given
L=3500.0*10**-10                  #m
h=6.62*10**-34
c=3*10**8

#Calculation
Hv=h*c/(L*(1.6*10**-19))

#Result
print"Energy of incident light is", round(Hv,3),"eV \nMetal B will yield photoelectrons."

Energy of incident light is 3.546 eV
Metal B will yield photoelectrons.


## Example 28.7 Page no 802¶

In [83]:
#Given
l=6000.0*10**-10             #m
h=6.62*10**-34                    #Js
e=1.6*10**-19
c=3*10**8

#Calculation
v0=c/l
w=(h*v0)/e

#Result
print"(i) Threshold frequency is", v0,"Hz"
print"(ii) Work function is",round(w,3),"eV"

(i) Threshold frequency is 5e+14 Hz
(ii) Work function is 2.069 eV


## Example 28.8 Page no 802¶

In [90]:
#Given
w=1.2*1.6*10**-19
l=5000.0*10**-10
c=3*10**8
h=6.62*10**-34
e=1.6*10**-19

#Calculation
A=((h*c)/l)-w
V0=A/e

#Result
print"Stopping potential is", round(V0,2),"V"

Stopping potential is 1.28 V


## Example 28.9 Page no 802¶

In [104]:
#Given
h=6.6*10**-34                     #Js
e=1.6*10**-19
l=500.0*10**-9                    #m

#Calculation
w=2*e
l0=(h*c)/w
E=((h*c)/l)-w
v0=E/e

#Result
print"(i) The threshold wavelength is", l0*10**9,"nm"
print"(ii) Maximum energy is",E*10**19,"*10**-19 J"
print"(iii) The stopping potential is",v0,"V"

(i) The threshold wavelength is 618.75 nm
(ii) Maximum energy is 0.76 *10**-19 J
(iii) The stopping potential is 0.475 V


## Example 28.10 Page no 802¶

In [109]:
#Given
V0=1.3
l=2271*10**-10
h=6.62*10**-34
e=1.6*10**-19
c=3*10**8

#Calculation
w=(h*c/l)-(V0*e)
l0=(h*c)/w

#Result
print"Work function of metal is", round(l0*10**10,0),"A"

Work function of metal is 2980.0 A


## Example 28.11 Page no 803¶

In [115]:
#Given
h=6.62*10**-34
c=3*10**8
l=640.2*10**-9
e=1.6*10**-19
V0=0.54
l1=427.2*10**-9

#Calculation
w=(h*c/l)-(e*V0)
v0=(((h*c)/l1)-w)/e

#Result
print"New stopping voltage is", round(v0,3),"V"

New stopping voltage is 1.507 V


## Example 28.12 Page no 803¶

In [121]:
#Given
l=5600.0*10**-10                      #m
h=6.625*10**-34
c=3*10**8
a=5

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

#Result
print"Number of visible light photon is", round(n*10**-19,2)*10**-19

Number of visible light photon is 1.41e-19


## Example 28.13 Page no 803¶

In [132]:
#Given
E=10**4                        #W
l=500.0                    #m
h=6.62*10**-34
A=0.4*10**-14                #m**2
i=10**-10                     #W/m**2
v=6*10**14

#Calculation
E1=E*l/(h*c)
E2=h*v
n=A/E2

#Result
print"(i) Number of photons emitted is",round(E1*10**-31,3)*10**31
print"(ii) Number of photons is", round(n*10**-4,0),"*10**4"

(i) Number of photons emitted is 2.518e+31
(ii) Number of photons is 1.0 *10**4


## Example 28.14 Page no 803¶

In [145]:
#Given
A=2*10**-4                        #m**2
An=10.0**-20
n1=5
i=10**-5                           #W/m**2

#Calculation
n=(A*n1)/An
E=i*A
E1=(E/n)/e
t=2/E1

#Result
print"Time required for the photoelectric emission is",t*10**-7,"*10**7 S"

Time required for the photoelectric emission is 1.6 *10**7 S