Wednesday, November 9, 2022

H C Verma solutions, PHOTOELECTRIC EFFECT AND WAVE-PARTICLE DUALITY, Chapter-42, OBJECTIVE-I, Concepts of Physics, Part-II

Photoelectric Effect and Wave-Particle Duality


OBJECTIVE - I


     1.  Plank Constant has the same dimensions as

(a) force x time 

(b) force x distance

(c) force x speed

(d) force x distance x time    


ANSWER: (d). 


Explanation: Plank Constant, 

h = E/𝝂

Dimensions of energy E are the same as

 Force x distance. 

 Unit of frequency 𝝂 is the number per unit of time. So the dimensions of h are the same as

  Force x distance x time.

Hence option (d) is correct.

 




     2.  Two photons having 

(a) equal wavelengths have equal linear momenta

(b) equal energies have equal linear momenta

(c) equal frequencies have equal linear momenta

(d) equal linear momenta have equal wavelengths.     


ANSWER: (d). 


Explanation: Linear momentum is a vector, that is it has a specific direction. While in the first three options, the magnitudes of linear momenta may be the same but the directions may be different. If their directions are different, they can not be said the same. Option (d) is correct. 



  



     3.  Let p and E denote the linear momentum and energy of a photon. If the wavelength is decreased, 

(a) both p and E increase 

(b) p increases and E decreases

(c) p decreases and E increases

(d) both p and E decrease.    


ANSWER: (a). 


Explanation: p = E/c and E =hc/λ.

So, p =h/λ.

Since h and c are constants, both p and E are inversely proportional to λ.

Thus if λ is decreased, both p and E increase. Option (a) is correct.



 



     4.  Let nᵣ and nᵦ be respectively the number of photons emitted by a red bulb and a blue bulb of equal power in a given time.

(a) nᵣ = nᵦ

(b) nᵣ < nᵦ

(c) nᵣ > nᵦ

(d) The information is insufficient to get a relation between nᵣ and nᵦ. 


ANSWER: (c). 


Explanation: Both the bulbs emit equal energy say 'E*' per second. So,

 nᵣEᵣ = nᵦEᵦ =E*    -------- (a) 

where Eᵣ and Eᵦ are energies of photons emitted by red and blue bulbs respectively.

Since energy of a photon = hc/λ, from (a),

nᵣhc/λᵣ = nᵦhc/λᵦ

→nᵣ/nᵦ =λᵣ/λᵦ

   We know that the wavelength of red light is more than the wavelength of blue light. Hence the number of photons emitted by the red bulb will be more than the number of photons emitted by the blue bulb. nᵣ > nᵦ. Option (c) is correct.


 



     5.  The equation E = pc is valid 

(a) for an electron as well as for a photon

(b) for an electron but not for a photon

(c) for a photon but not for an electron

(d) neither for an electron nor for a photon.   


ANSWER: (c). 


Explanation: Equation E = pc is valid for a particle that has zero rest mass. Since a photon has zero rest mass but an electron has a rest mass. So it is only correct for a photon. Option (c) is correct. 



     



     6.  The work function of a metal is h𝝂ₒ. Light of frequency 𝝂 falls on this metal. The photoelectric effect will take place only if

(a) 𝝂 ≥ 𝝂ₒ

(b) 𝝂 > 2𝝂ₒ

(c) 𝝂 < 𝝂ₒ

(d) 𝝂 < 𝝂ₒ/2. 


ANSWER: (a). 


Explanation: Work function is the minimum energy required to detach an electron from the surface of a metal. The energy of an incident photon is h𝝂. This energy should be more than or equal to the work function for the emission of a photoelectron. So, 

h𝝂 ≥ h𝝂ₒ  

→ 𝝂 ≥ 𝝂ₒ 

Option (a) is correct.




 


     7.  Light of wavelength λ falls on a metal having work function hc/λₒ. The photoelectric effect will take place only if 

(a) λ ≥ λₒ

(b) λ ≥ 2λₒ

(c) λ ≤ λₒ

(d) λ < λₒ/2. 


ANSWER: (c). 


Explanation: The energy of a photon having wavelength λ is  

 =hc/λ. 

The photoelectric effect will take place only if this energy is greater than or equal to the work function, So,

 hc/λ ≥ hc/λₒ

→1/λ ≥ 1/λₒ

→λ ≤ λₒ

Option (c) is correct.



 


     8.  When stopping potential is applied in an experiment on the photoelectric effect, no photocurrent is observed. This means that 

(a) the emission of photoelectrons is stopped. 

(b) the photoelectrons are emitted but are reabsorbed by the emitter metal 

(c) the photoelectrons are accumulated near the collector plate

(d) the photoelectrons are dispersed from the sides of the apparatus.     


ANSWER: (b). 


Explanation: When photons of light having energies more than the work function of a metal are incident upon it, photoelectrons are emitted. Out of the total energy of a photon, energy equal to the work function is used just to take the electron out of the metal, and the rest of the energy is used as the kinetic energy of the electron. Due to this kinetic energy, the electron moves to the other end of the apparatus where it is collected and the photocurrent starts. 

    When stopping potential is applied, the collecting plate is made negative compared to the emitter plate. This repels the photoelectrons towards the emitter plate and some of them are reabsorbed there. Thus the photocurrent stops. Option (b) is correct. 


  



     9.  If the frequency of light in a photoelectric experiment is doubled, the stopping potential will 

(a) be doubled

(b) be halved

(c) become more than double

(d) become less than double.   


ANSWER: (c). 


Explanation: If V is stopping potential and φ the work function, then 

eV = h𝝂 -φ

→V = (h𝝂-φ)/e

If the frequency of the light is doubled to 2𝝂, let the stopping potential be equal to V'. So, 

V' = (2h𝝂-φ)/e

    ={(2h𝝂-2φ) +φ}/e

    =2(h𝝂-φ)/e +φ/e

    =2V +φ/e

So V' is more than 2V. Option (c) is correct.


     



     10.  The frequency and intensity of a light source are both doubled. Consider the following statements.

(A) The saturation photocurrent remains almost the same. 

(B) The maximum kinetic energy of the photoelectrons is doubled.

 

(a) Both A and B are true. 

(b) A is true but B is false. 

(c) A is false but B is true. 

(d) Both A and b are false.        


ANSWER: (b). 


Explanation: Keeping frequency constant, if the intensity of light is increased then the number of photons increases resulting in more photoelectrons. This increases the photocurrent. But when we double the frequency of light, the intensity is also doubled, which means the number of photons does not increase. Each photon now carries double energy and the intensity of light is the energy falling on a unit area in unit time. Since the number of photons is not increasing, the number of photoelectrons is also not increasing. The saturation photocurrent will be almost the same. Statement A is correct. 

    The increased energies of the photons will be used to increase the maximum kinetic energy of the emitted photoelectrons. 

Kₘₐᵪ =h𝝂 -φ, where φ is the work function.

If the frequency is doubled as in this case,

K'ₘₐᵪ =2h𝝂 -φ

Clearly, the last one is not double the original maximum kinetic energy. Statement B is incorrect.

  Option (b) is correct. 



 



     11.  A point source of light is used in a photoelectric effect. If the source is removed farther from the emitting metal, the stopping potential 

(a) will increase 

(b) will decrease

(c) will remain constant

(d) will either increase or decrease.    


ANSWER: (c). 


Explanation: When the point source of light is moved farther from the metal, the intensity of light near the metal will decrease but the frequency remains the same. The stopping potential depends on the frequency of light, not on the intensity. So the stopping potential will remain constant in this case. Option (c) is correct. 



   



     12.  A point source causes a photoelectric effect from a small metal plate. Which of the following curves may represent the saturation photocurrent as a function of the distance between the source and the metal?  
The figure for Q-12

 

ANSWER: (d). 


Explanation: If the point source emits energy E per second then the intensity of light at distance r  is 

I =E/4πr². 

Since the saturation photocurrent, 'i' is directly proportional to intensity, so 

  i ∝ 1/r².

This relationship is best represented by curve d in the figure.

Option (d) is correct.



 



     13. Nonmonochromatic light is used in an experiment on the photoelectric effect. The stopping potential

(a) is related to the mean wavelength

(b) is related to the longest wavelength

(c) is related to the shortest wavelength

(d) is not related to the wavelength.    


ANSWER: (c). 


Explanation: Stopping potential depends on the wavelength of the light. The smaller the wavelength, the greater the energy of the photons, and hence more the stopping potential. To stop the photocurrent in this case, photoelectrons resulting from the shortest wavelength of photons should be stopped. 

   Option (c) is correct.


 



     14.  A proton and an electron are accelerated by the same potential difference. Let λₑ and λₚ denote the de Broglie wavelengths of the electron and proton respectively. 

(a) λₑ = λₚ

(b) λₑ < λₚ

(c) λₑ > λₚ

(d) The relation between λₑ and λₚ depends on the accelerating potential difference.

 


ANSWER: (c). 


Explanation: When a proton and an electron are accelerated through the same potential difference, they gain the same kinetic energies because of the same magnitude of the charge. If v is the speed gained by the electron through a potential difference of V then, 

½mₑv² =eV

→(mₑv)² =2mₑeV

→pₑ =√(2mₑeV)

Where pₑ is the momentum of the electron.

Similarly, the momentum of the proton 

pₚ =√(2mₚeV)

Since the mass of a proton is more than the mass of an electron, so

pₚ > pₑ

Now de Broglie's wavelength is given as, 

λ = h/p,

Electron's wavelength λₑ  =h/pₑ

Proton's wavelength λₚ =h/pₚ

Clearly, λₑ > λₚ.

Option (c) is correct.

 

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Links to the Chapters




CHAPTER- 42- Photoelectric Effect and Wave-Particle Duality



CHAPTER- 34- Magnetic Field

CHAPTER- 29- Electric Field and Potential











CHAPTER- 28- Heat Transfer

OBJECTIVE -I







EXERCISES - Q51 to Q55


CHAPTER- 27-Specific Heat Capacities of Gases

CHAPTER- 26-Laws of Thermodynamics


CHAPTER- 25-CALORIMETRY

Questions for Short Answer

OBJECTIVE-I

OBJECTIVE-II


EXERCISES - Q-11 to Q-18


CHAPTER- 24-Kinetic Theory of Gases







CHAPTER- 23 - Heat and Temperature






CHAPTER- 17 - Light Waves




CHAPTER- 14 - Fluid Mechanics




CHAPTER- 13 - Fluid Mechanics


CHAPTER- 12 - Simple Harmonic Motion









CHAPTER- 11 - Gravitation





CHAPTER- 10 - Rotational Mechanics






CHAPTER- 9 - Center of Mass, Linear Momentum, Collision


CHAPTER- 8 - Work and Energy

Click here for → Question for Short Answers

Click here for → OBJECTIVE-I

Click here for → OBJECTIVE-II

Click here for → Exercises (1-10)

Click here for → Exercises (11-20)

Click here for → Exercises (21-30)

Click here for → Exercises (31-42)

Click here for → Exercise(43-54)

CHAPTER- 7 - Circular Motion

Click here for → Questions for Short Answer 

Click here for → OBJECTIVE-I

Click here for → OBJECTIVE-II

Click here for → EXERCISES (1-10)

Click here for → EXERCISES (11-20)

Click here for → EXERCISES (21-30)

CHAPTER- 6 - Friction

Click here for → Questions for Short Answer

Click here for → OBJECTIVE-I

Click here for → Friction - OBJECTIVE-II

Click here for → EXERCISES (1-10)

Click here for → Exercises (11-20)

Click here for → EXERCISES (21-31)

For more practice on problems on friction solve these- "New Questions on Friction".

---------------------------------------------------------------------------------

CHAPTER- 5 - Newton's Laws of Motion


Click here for → QUESTIONS FOR SHORT ANSWER

Click here for→Newton's Laws of Motion,Exercises(Q.No. 13 to 27)

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CHAPTER- 4 - The Forces

The Forces-

"Questions for short Answers"    


Click here for "The Forces" - OBJECTIVE-I


Click here for "The Forces" - OBJECTIVE-II


Click here for "The Forces" - Exercises


--------------------------------------------------------------------------------------------------------------

CHAPTER- 3 - Kinematics - Rest and Motion

Click here for "Questions for short Answers"


Click here for "OBJECTIVE-I"


Click here for EXERCISES (Question number 1 to 10)


Click here for EXERCISES (Question number 11 to 20)


Click here for EXERCISES (Question number 21 to 30)


Click here for EXERCISES (Question number 31 to 40)


Click here for EXERCISES (Question number 41 to 52)


CHAPTER- 2 - "Physics and Mathematics"

Click here for "Questions for Short Answers"


Click here for "OBJECTIVE-II"

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