Dual Nature of Radiation and Matter: JEE Main Previous Year Questions (2021-2026)

 Page 1


JEE Main Previous Year Questions (2021-2026): 
Dual Nature of Radiation  
 
(January 2026) 
 
Q1: Number of photons of equal energy emitted per second by a 6 mW laser source 
operating at 663 nm is ________.  
(Given : h = 6.63 × 10
-34
 J.s and c = 3 × 10
8
 m/s)  
(a) 10 × 10
15  
(b) 5 × 10
16
  
(c) 5 × 10
15
  
(d) 2 × 10
16
  
Ans: (d) 
Sol:  
The power (P) of the laser source is, P = 6 mW = 6 × 10
-3
 J / s  
The wavelength (?) of the emitted photon is ? = 663 nm = 663 × 10
-9
 m  
Planck's constant h = 6.63 × 10
-34
 J · s  
Speed of light c = 3 × 10
8
 m / s  
The energy of a single photon is given by : 
 
Total Power is the number of photons per second multiplied by the energy of one photon: 
 
Substituting the given values into the equation : 
Page 2


JEE Main Previous Year Questions (2021-2026): 
Dual Nature of Radiation  
 
(January 2026) 
 
Q1: Number of photons of equal energy emitted per second by a 6 mW laser source 
operating at 663 nm is ________.  
(Given : h = 6.63 × 10
-34
 J.s and c = 3 × 10
8
 m/s)  
(a) 10 × 10
15  
(b) 5 × 10
16
  
(c) 5 × 10
15
  
(d) 2 × 10
16
  
Ans: (d) 
Sol:  
The power (P) of the laser source is, P = 6 mW = 6 × 10
-3
 J / s  
The wavelength (?) of the emitted photon is ? = 663 nm = 663 × 10
-9
 m  
Planck's constant h = 6.63 × 10
-34
 J · s  
Speed of light c = 3 × 10
8
 m / s  
The energy of a single photon is given by : 
 
Total Power is the number of photons per second multiplied by the energy of one photon: 
 
Substituting the given values into the equation : 
 
Therefore, the laser source emits 2 × 10
16
 photons every second. Hence, the correct option is 
(d). 
 
Q2: When a light of a given wavelength falls on a metallic surface the stopping potential 
for photoelectrons is 3.2. If a second light having wavelength twice of first light is used, 
the stopping potential drops to 0.7 V. The wavelength of first light is _______m. 
(h = 6.63 × 10
-34
J.s,e = 1.6 × 10
-19
C, c = 3 × 10
8
m/s) 
(a) 2.9 × 10
-8 
(b) 2.5 × 10
-7 
(c) 3.1 × 10
-7 
(d) 2.2 × 10
-8 
Ans: (b) 
Sol: 
When a light of wavelength (?) is incident on a metal of work function ? then the maximum 
kinetic energy of the photo-electron is given by Einstein's photoelectric equation: 
 
where V
s
 is the stopping potential and ? is the work function of the metal. 
Case 1 : Wavelength is ? , stopping potential is 3.2 V. 
 
Case 2 : Wavelength is 2 ? , stopping potential is 0.7 V . 
Page 3


JEE Main Previous Year Questions (2021-2026): 
Dual Nature of Radiation  
 
(January 2026) 
 
Q1: Number of photons of equal energy emitted per second by a 6 mW laser source 
operating at 663 nm is ________.  
(Given : h = 6.63 × 10
-34
 J.s and c = 3 × 10
8
 m/s)  
(a) 10 × 10
15  
(b) 5 × 10
16
  
(c) 5 × 10
15
  
(d) 2 × 10
16
  
Ans: (d) 
Sol:  
The power (P) of the laser source is, P = 6 mW = 6 × 10
-3
 J / s  
The wavelength (?) of the emitted photon is ? = 663 nm = 663 × 10
-9
 m  
Planck's constant h = 6.63 × 10
-34
 J · s  
Speed of light c = 3 × 10
8
 m / s  
The energy of a single photon is given by : 
 
Total Power is the number of photons per second multiplied by the energy of one photon: 
 
Substituting the given values into the equation : 
 
Therefore, the laser source emits 2 × 10
16
 photons every second. Hence, the correct option is 
(d). 
 
Q2: When a light of a given wavelength falls on a metallic surface the stopping potential 
for photoelectrons is 3.2. If a second light having wavelength twice of first light is used, 
the stopping potential drops to 0.7 V. The wavelength of first light is _______m. 
(h = 6.63 × 10
-34
J.s,e = 1.6 × 10
-19
C, c = 3 × 10
8
m/s) 
(a) 2.9 × 10
-8 
(b) 2.5 × 10
-7 
(c) 3.1 × 10
-7 
(d) 2.2 × 10
-8 
Ans: (b) 
Sol: 
When a light of wavelength (?) is incident on a metal of work function ? then the maximum 
kinetic energy of the photo-electron is given by Einstein's photoelectric equation: 
 
where V
s
 is the stopping potential and ? is the work function of the metal. 
Case 1 : Wavelength is ? , stopping potential is 3.2 V. 
 
Case 2 : Wavelength is 2 ? , stopping potential is 0.7 V . 
 
Subtracting equation (ii) from equation (i) : 
 
Substituting the given values : 
 
Therefore, the initial wavelength of light used was 2.5 × 10 
-7
 m.  
Hence, the correct option is (b). 
 
Q3: The de Broglie wavelength of an oxygen molecule at 27
°
C is x × 10
-12
m. The value of 
x is (take Planck's constant = 6.63 × 10
-34
 J. s, Boltzmann constant = 1.38 × 10
-23
 J / K, 
mass of oxygen molecule = 5.31 × 10
-26
 kg)  
(a) 24  
(b) 30  
(c) 20  
(d) 26  
Ans: (d) 
Sol:  
For a gas molecule, the average kinetic energy (K) is given by kinetic theory: 
 
where k
B
 is the Boltzmann constant and T is the absolute temperature. 
The relationship between momentum (p) and kinetic energy (K) is: 
 
Page 4


JEE Main Previous Year Questions (2021-2026): 
Dual Nature of Radiation  
 
(January 2026) 
 
Q1: Number of photons of equal energy emitted per second by a 6 mW laser source 
operating at 663 nm is ________.  
(Given : h = 6.63 × 10
-34
 J.s and c = 3 × 10
8
 m/s)  
(a) 10 × 10
15  
(b) 5 × 10
16
  
(c) 5 × 10
15
  
(d) 2 × 10
16
  
Ans: (d) 
Sol:  
The power (P) of the laser source is, P = 6 mW = 6 × 10
-3
 J / s  
The wavelength (?) of the emitted photon is ? = 663 nm = 663 × 10
-9
 m  
Planck's constant h = 6.63 × 10
-34
 J · s  
Speed of light c = 3 × 10
8
 m / s  
The energy of a single photon is given by : 
 
Total Power is the number of photons per second multiplied by the energy of one photon: 
 
Substituting the given values into the equation : 
 
Therefore, the laser source emits 2 × 10
16
 photons every second. Hence, the correct option is 
(d). 
 
Q2: When a light of a given wavelength falls on a metallic surface the stopping potential 
for photoelectrons is 3.2. If a second light having wavelength twice of first light is used, 
the stopping potential drops to 0.7 V. The wavelength of first light is _______m. 
(h = 6.63 × 10
-34
J.s,e = 1.6 × 10
-19
C, c = 3 × 10
8
m/s) 
(a) 2.9 × 10
-8 
(b) 2.5 × 10
-7 
(c) 3.1 × 10
-7 
(d) 2.2 × 10
-8 
Ans: (b) 
Sol: 
When a light of wavelength (?) is incident on a metal of work function ? then the maximum 
kinetic energy of the photo-electron is given by Einstein's photoelectric equation: 
 
where V
s
 is the stopping potential and ? is the work function of the metal. 
Case 1 : Wavelength is ? , stopping potential is 3.2 V. 
 
Case 2 : Wavelength is 2 ? , stopping potential is 0.7 V . 
 
Subtracting equation (ii) from equation (i) : 
 
Substituting the given values : 
 
Therefore, the initial wavelength of light used was 2.5 × 10 
-7
 m.  
Hence, the correct option is (b). 
 
Q3: The de Broglie wavelength of an oxygen molecule at 27
°
C is x × 10
-12
m. The value of 
x is (take Planck's constant = 6.63 × 10
-34
 J. s, Boltzmann constant = 1.38 × 10
-23
 J / K, 
mass of oxygen molecule = 5.31 × 10
-26
 kg)  
(a) 24  
(b) 30  
(c) 20  
(d) 26  
Ans: (d) 
Sol:  
For a gas molecule, the average kinetic energy (K) is given by kinetic theory: 
 
where k
B
 is the Boltzmann constant and T is the absolute temperature. 
The relationship between momentum (p) and kinetic energy (K) is: 
 
Substituting K: 
 
The de Broglie wavelength is defined as: 
 
From both the relations, 
 
The given temperature is 27
°
C.  
T = 27 + 273 = 300 K  
The given mass is 5.31 × 10 
-26
 kg.  
So, the de Broglie wavelength is, 
 
 
Therefore, the value of x is 26.  
Hence, the correct option is (d). 
 
Q4: Light is incident on a metallic plate having work function 110 × 10
-20
J. If the produced 
photoelectrons have zero kinetic energy then the angular frequency of the incident light 
is _____ rad/s. (h = 6.63 × 10
-34
 J.s).  
(a) 1.04 × 10
13
  
(b) 1.66 × 10
16
  
(c) 1.66 × 10
15
  
(d) 1.04 × 10
16 
Ans: (d) 
Sol: 
Page 5


JEE Main Previous Year Questions (2021-2026): 
Dual Nature of Radiation  
 
(January 2026) 
 
Q1: Number of photons of equal energy emitted per second by a 6 mW laser source 
operating at 663 nm is ________.  
(Given : h = 6.63 × 10
-34
 J.s and c = 3 × 10
8
 m/s)  
(a) 10 × 10
15  
(b) 5 × 10
16
  
(c) 5 × 10
15
  
(d) 2 × 10
16
  
Ans: (d) 
Sol:  
The power (P) of the laser source is, P = 6 mW = 6 × 10
-3
 J / s  
The wavelength (?) of the emitted photon is ? = 663 nm = 663 × 10
-9
 m  
Planck's constant h = 6.63 × 10
-34
 J · s  
Speed of light c = 3 × 10
8
 m / s  
The energy of a single photon is given by : 
 
Total Power is the number of photons per second multiplied by the energy of one photon: 
 
Substituting the given values into the equation : 
 
Therefore, the laser source emits 2 × 10
16
 photons every second. Hence, the correct option is 
(d). 
 
Q2: When a light of a given wavelength falls on a metallic surface the stopping potential 
for photoelectrons is 3.2. If a second light having wavelength twice of first light is used, 
the stopping potential drops to 0.7 V. The wavelength of first light is _______m. 
(h = 6.63 × 10
-34
J.s,e = 1.6 × 10
-19
C, c = 3 × 10
8
m/s) 
(a) 2.9 × 10
-8 
(b) 2.5 × 10
-7 
(c) 3.1 × 10
-7 
(d) 2.2 × 10
-8 
Ans: (b) 
Sol: 
When a light of wavelength (?) is incident on a metal of work function ? then the maximum 
kinetic energy of the photo-electron is given by Einstein's photoelectric equation: 
 
where V
s
 is the stopping potential and ? is the work function of the metal. 
Case 1 : Wavelength is ? , stopping potential is 3.2 V. 
 
Case 2 : Wavelength is 2 ? , stopping potential is 0.7 V . 
 
Subtracting equation (ii) from equation (i) : 
 
Substituting the given values : 
 
Therefore, the initial wavelength of light used was 2.5 × 10 
-7
 m.  
Hence, the correct option is (b). 
 
Q3: The de Broglie wavelength of an oxygen molecule at 27
°
C is x × 10
-12
m. The value of 
x is (take Planck's constant = 6.63 × 10
-34
 J. s, Boltzmann constant = 1.38 × 10
-23
 J / K, 
mass of oxygen molecule = 5.31 × 10
-26
 kg)  
(a) 24  
(b) 30  
(c) 20  
(d) 26  
Ans: (d) 
Sol:  
For a gas molecule, the average kinetic energy (K) is given by kinetic theory: 
 
where k
B
 is the Boltzmann constant and T is the absolute temperature. 
The relationship between momentum (p) and kinetic energy (K) is: 
 
Substituting K: 
 
The de Broglie wavelength is defined as: 
 
From both the relations, 
 
The given temperature is 27
°
C.  
T = 27 + 273 = 300 K  
The given mass is 5.31 × 10 
-26
 kg.  
So, the de Broglie wavelength is, 
 
 
Therefore, the value of x is 26.  
Hence, the correct option is (d). 
 
Q4: Light is incident on a metallic plate having work function 110 × 10
-20
J. If the produced 
photoelectrons have zero kinetic energy then the angular frequency of the incident light 
is _____ rad/s. (h = 6.63 × 10
-34
 J.s).  
(a) 1.04 × 10
13
  
(b) 1.66 × 10
16
  
(c) 1.66 × 10
15
  
(d) 1.04 × 10
16 
Ans: (d) 
Sol: 
The energy of the incident photon (E) is used to overcome the work function (F) of the metal, 
and the remaining energy becomes the maximum kinetic energy (K
max
) of the emitted 
photoelectron:  
K
max
 = E - F  
It is given that the produced photoelectrons have exactly zero kinetic energy (K
max
 = 0). This 
means the energy of the incident light is exactly equal to the work function of the metal (this 
corresponds to the threshold frequency). 
0 = E - F 
 
The energy of a photon is given by E = hf , where h is Planck's constant and f is the linear 
frequency.  
Using the relationship between linear frequency (f) and angular frequency (?):  
  
So, the expression for the energy of a photon is, 
 
From relations (i) and (iii) 
 
Work function of metal is,  
The Planck's constant is,