Wednesday, November 2, 2022

H C Verma solutions, PHOTOELECTRIC EFFECT AND WAVE-PARTICLE DUALITY, Chapter-42, Questions for Short Answer, Concepts of Physics, Part-II

Photoelectric Effect and Wave-Particle Duality


Questions for Short Answer


     1.  Can we find the mass of a photon by the definition p =mv? 

ANSWER: p =mv is the momentum of a particle according to classical physics. In classical physics, light/electromagnetic radiation is a wave propagation, and it does not have a mass. The photon name itself is the result of quantum physics. According to this theory,

The momentum of a photon is not due to its mass (mass is assumed to be zero) but it is without its mass. The energy of a photon E is given as, 

E²  =(mc²)²+(pc)²  

Since mass id zero, E =pc. 

→p =E/c. Clearly, this momentum is not due to its mass. So we can not find the mass of a photon by p =mv.


 




     2.  Is it always true that for two sources of equal intensity, the number of photons emitted in a given time is equal?  

ANSWER: The intensity of light is the energy passing normally to a unit area in unit time. Two light sources may have the same intensity even if they have different wavelengths. In this case, the number of photons emitted in a given time will be different because the energy of a photon depends on its wavelength. Only if the wavelengths are the same, the number will be the same.


 




     3.  What is the speed of a photon with respect to another photon if (a) the two photons are going in the same direction and (b) they are going in opposite directions? 

ANSWER: A photon always travels at a speed equal to the speed of light c. This is true for any frame of reference used to observe the photon. So in both the given conditions, if we chose one photon as a frame of reference to get the relative speed of the other one, its speed will always be equal to c.  


 




     4.  Can a photon be deflected by an electric field? By a magnetic field? 

ANSWER: Since a photon is electrically or magnetically neutral, it will neither be deflected by an electric field nor by a magnetic field.  




     5.  A hot body is kept in a closed room maintained at a lower temperature. Is the number of photons in the room increasing? 

ANSWER: Photons are not like objects that can be kept in a closed room. The hot body will radiate a part of losing heat in the form of electromagnetic radiation that essentially is through photons. These photons will strike room walls and will be absorbed there. Soon there will be a balance there and if the temperature of the hot body is maintained, the number of photons emitted and absorbed will be equal. Thus at any instant, the number of photons will be constant. 


 




     6.  Should the energy of a photon be called its kinetic energy or its internal energy? 

ANSWER: A photon is itself a quantum of energy. It has no mass and always a speed equal to c. The energy associated with a photon is due to its frequency and it is equal to h𝛎. According to classical physics, the kinetic energy of an object depends on its mass and velocity. Photons have zero mass and constant velocity c but different photons of different frequencies have different energies. On this basis, its energy can not be called kinetic energy.  

  A photon has no internal structure hence it has no internal energy. 

  So a photon is itself a packet of energy that depends on its frequency.  


   




     7.  In an experiment on the photoelectric effect, a photon is incident on an electron from one direction and the photoelectron is emitted almost in opposite direction. Does this violet conservation of momentum? 

ANSWER: We must not forget that the colliding electron is not an independent electron but it is a part of an atom. When considering the conservation of momentum, we should count the incident photon and the atom as a system. Total energy and total momentum are conserved in such collisions. Thus there is no violation of the conservation of momentum. 



  




     8.  It is found that yellow light does not eject photoelectrons from a metal. Is it advisable to try with orange light? With a green light? 

ANSWER: Since yellow light does not eject photoelectrons from metal, it means that the frequency of yellow light is less than the threshold frequency of the metal. We need a greater frequency of light to get photoelectrons. Since the frequency of the orange light is less than the yellow light it is not advisable to try this one. The frequency of the green light is more than that yellow light, so there is a chance to get photoelectrons. Hence it is advisable to try the green light. 


 




     9.  It is found that photosynthesis starts in certain plants when exposed to sunlight but it does not start if the plant is exposed only to infrared light. Explain. 

ANSWER: Photosynthesis in plants starts with the help of a substance called chlorophyll that is present in green leaves. It needs a photon of sufficient energy to be absorbed by its electron and get excited to be released. This breaks the water molecule and with the presence of carbon dioxide photosynthesis starts. The sunlight has photons of sufficient energy to excite the chlorophyll molecules and begin the process but infrared light has a lower frequency than sunlight and its photons have lower energies. These photons are unable to excite the chlorophyll molecules and photosynthesis does not start.    




     10.  The threshold wavelength of a metal is λₒ. Light of wavelength slightly less than λₒ is incident on an insulated plate made of this metal. It is found that photoelectrons are emitted for some time and after that, the emission stops. Explain. 

ANSWER: The energy of light of wavelength slightly less than the threshold wavelength λₒ will have energy more than the work function. So the photoelectrons start to emit from the surface of the insulated metal plate after getting energy from the incident photons. These are the detected photoelectrons. Since the plate is insulated the deficiency of the electrons can not be filled. Thus a net positive charge will be there on the surface of the plate. So further electrons can not get out of the surface due to the electrostatic attraction and the emission of photoelectrons stops.


  




     11.  Is p =E/c valid for electrons? 

ANSWER: No. The photons have constant speed 'c', and the energy of each photon is E =hc/λ. Since the momentum of a photon is p =h/λ, hence E =pc

→p =E/c.

  But the electrons have speeds much less than 'c', so E ≠ hc/λ. So p =E/c is not valid for electrons.


 




     12.  Consider the de Broglie wavelength of an electron and a proton. Which wavelength is smaller if the two particles have (a) the same speed (b) the same momentum (c) the same energy? 

ANSWER: De Broglie's wavelength is, 

λ =h/p,

where h is Plank's constant and p is the momentum of the particle.

(a) Since a proton is much heavier than an electron, the proton will have greater momentum than the electron for the same speed. Clearly, the proton will have a smaller wavelength.


(b) When both have the same momentum p, wavelength λ =h/p will be the same for both.

 

(c) For two particles having mass m and m', speed v and v', if both have equal kinetic energy then,

mv² =m'v'²

Multiplying both sides by mm', we get

mm'mv² =mm'm'v'²

→m²v²m' =m'²v'²m

→p²m' =p'²m

Where p is the momentum of the particle having m and p' for particle m'.

→(p'/p)² =m'/m 

→p'/p =√(m'/m)

If m' > m then p' > p.

Since the mass of the proton > the mass of the electron, the momentum of the proton > the momentum of the electron for equal energy. 

We have, λ =h/p, hence the wavelength of the proton will be less than the wavelength of the electron for equal energy. 


 




     13.  If an electron has a wavelength, does it also have a color? 

ANSWER: The color we see is due to those electromagnetic waves that have wavelengths within a certain range that strike our retina and excite it. The wavelength associated with an electron is not the wavelength of an electromagnetic wave but it is that of de Broglie's waves. Hence it has no color.  

 

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Links to the Chapters







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"

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Click here for "OBJECTIVE-II"

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