Tuesday, November 15, 2022

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

Photoelectric Effect and Wave-Particle Duality


OBJECTIVE - II


     1.  When the intensity of a light source is increased,

(a) the number of photons emitted by the source in unit time increases

(b) the total energy of the photons emitted per unit of time increases

(c) more energetic photons are emitted

(d) faster photons are emitted.    


ANSWER: (a), (b). 


Explanation: When the intensity of light is increased, it means the energy emitted by the light source per unit of time is increased without changing the wavelength of emitted light. This increase in energy is achieved by increasing the number of photons emitted in a unit of time. Since the wavelength is the same, the energy of an individual photon remains the same but the total energy of photons emitted per unit of time increases due to an increase in the number of photons. So options (a) and (b) are correct but (c) are incorrect. 

  Since the speed of photons is always the same whatever may be the wavelength, there is no question of faster photons. Option (d) is not correct.






     2.  The photoelectric effect supports the quantum nature of light because 

(a) there is a minimum frequency below which no photoelectrons are emitted

(b) the maximum kinetic energy of photoelectrons depends only on the frequency of light and not its intensity

(c) even when the metal surface is  faintly illuminated the photoelectrons leave the surface immediately

(d) the electric charge of the photoelectrons is quantized.   


ANSWER: (a), (b), (c). 


Explanation: If the quantum nature of light were not true, the maximum kinetic energy should be dependent on the intensity because the intensity is the amount of energy falling on a unit area of a cross-section in a unit of time. Also, photoelectrons should be emitted with any wavelength by just changing the intensity. But it is not found true. The energy of a photon is dependent on its frequency. A photoelectron is emitted from a particular surface only if a minimum amount of energy is gained by it through the photon. So for this photo effect to take place a minimum frequency of the photon is required. So even if the surface is faintly illuminated with this frequency or a higher frequency of photons, photoelectrons leave the surface immediately. If the higher frequency of the photons is incident on the surface than the required frequency, maximum kinetic energy is increased. 

Thus the energy of photons is quantized and related to the frequency. The options (a), (b) and (c) are correct. 

The electric charge of a photoelectron is constant. Option (d) is not correct. 






     3.  A photon of energy h𝜈 is absorbed by a free electron of a metal having work function φ <h𝜈. 

(a) the electron is sure to come out.

(b) the electron is sure to come out with kinetic energy h𝜈-φ

(c) either the electron does not come out or it comes out with a kinetic energy h𝜈-φ.

(d) it may come out with kinetic energy less than h𝜈-φ. 


ANSWER: (d). 


Explanation: When the free electron of a metal absorbs a photon of energy h𝜈, it gets a kinetic energy =h𝜈-φ, but it may lose some of the absorbed kinetic energy due to collision with adjacent molecules. So it may come out with kinetic energy =h𝜈 -φ. Option (d) is correct. 





     4.  If the wavelength of light in an experiment on the photoelectric effect is doubled, 

(a) the photoelectric emission will not take place 

(b) the photoelectric emission may or may not take place

(c) the stopping potential will increase 

(d) the stopping potential will decrease.


ANSWER: (b), (d). 


Explanation: With a doubled wavelength, the energy of photons will be halved because E =hc/λ. Only if the halved energy is more than the work function, photoelectric emission may take place. So option (b) is correct. 

    The maximum kinetic energy of electrons (hc/𝜆 -φ) will get decreased hence less stopping potential will be needed. Option (d) is correct.   





     5.  The photocurrent in an experiment on the photoelectric effect increases if 

(a) the intensity of the source is increased

(b) the exposure time is increased

(c) the intensity of the source is decreased

(d) the exposure time is decreased.    


ANSWER: (a). 


Explanation: Photocurrent will increase if the number of photoelectrons increases. The number of photoelectrons will increase if the number of photons increases. The number of photons will increase if the intensity of the source is increased. Photocurrent does not depend on exposure time. Option (a) is correct. 





     6.  The collector plate in an experiment on the photoelectric effect is kept vertically above the emitter plate. The light source is put on and a saturation photocurrent is recorded. An electric field is switched on which has a vertically downward direction.  

(a) the photocurrent will increase

(b) the kinetic energy of electrons will increase

(c) the stopping potential will decrease

(d) the threshold wavelength will increase. 


ANSWER: (b). 


Explanation: Since the direction of the electric field is downwards, it will apply an upward force on the emitted photoelectrons. The kinetic energy of photoelectrons will increase. Option (b) is correct. The current depends on the number of electrons emitted per unit of time which is not changing here. So photocurrent will not increase. Option (a) is not correct. Since kinetic energy increases, the stopping potential will increase, not decrease. Option (c) is not correct.

  Threshold wavelength is a property of the emitter surface, so it will not change with the application of an electric field. Option (d) is not correct.    





     7.  In which of the following situations does the heavier of the two particles have a smaller de Broglie wavelength? The two particles

(a) move with the same speed
(b) move with the same linear momentum

(c) move with the same kinetic energy

(d) have fallen through the same height.    


ANSWER: (a), (c), (d). 


Explanation: De Broglie's wavelength is, 

𝜆 =h/p, where p is the linear momentum. 

When both particles have the same speed, the linear momentum of a heavier particle will be more. So de Broglie wavelength of the heavier particle will be smaller. Option (a) is correct. 

  When both particles have the same linear momentum p, they both have the same de Broglie wavelength, 

𝜆 =h/p. Option (b) is incorrect.

   Kinetic energy, K =½mv²

  →K =½(mv)²/m =p²/2m

  →p =√(2mK)

So the heavier particle will have greater linear momentum and hence the shorter de Broglie wavelength 𝜆. Option (c) is correct.

     When two particles fall through the same height their speeds are the same. As in option (a), the heavier particles will have greater linear momentum p and hence the smaller wavelength 𝜆. Option (d) is also 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".

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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


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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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