Friday, August 18, 2023

H C Verma solutions, The Nucleus, Chapter-46, Questions for Short Answer, Concepts of Physics, Part-II

Questions for Short Answer


       1. If neutrons exert only attractive force, why don't we have a nucleus containing neutrons alone?   

ANSWER: The nucleus is at the center of an atom where most of its mass is concentrated whereas the rest of its mass is associated with electrons that revolve around the nucleus. Electrons are bound to the nucleus due to the electrostatic force of attraction because the electrons have a negative electric charge and protons at the nucleus have a positive charge.
    The neutrons have an attractive force due to the close-range nuclear forces which decrease very rapidly with the distance. The effect of this force is so negligible at the distance of electrons that they can not revolve around the neutrons under this force because there is no electrostatic force of attraction due to electrically neutral neutrons. So only neutrons can not make a nucleus of an atom. 






       2. Consider two pairs of neutrons. In each pair, the separation between the neutrons is the same. Can the force between the neutrons have different magnitudes for the two pairs?   

ANSWER: If the two pairs of neutrons are far away from the influence of other particles, then the magnitude of forces between them will be the same. It may differ if each of the pairs is part of some nucleus.    





       3. A molecule of hydrogen contains two protons and two electrons. The nuclear force between these two protons is always neglected while discussing the behavior of a hydrogen molecule. Why?   

ANSWER: A molecule of hydrogen contains two hydrogen atoms that are bound to each other due to sharing of one orbiting electron of each atom. So the distance between two protons is about the diameter of a hydrogen atom. At this distance, the close-range attractive nuclear force has no effect. Due to the presence of an electron in the orbit which has an equal and opposite electric charge, a hydrogen atom is electrically neutral and the repulsive electrostatic force between the protons is neutralized by the orbiting electrons. 
   So the nuclear force between the two protons in a hydrogen molecule is always neglected while discussing the behavior of a hydrogen molecule. 
 





       4. Is it easier to take out a nucleon from carbon or from iron? From iron or from lead?   

ANSWER: Binding energy per nucleon is the energy required to take out a nucleon from a nucleus. We know that this energy is highest in the zone of mass number 50 to 80. It decreases before and after this zone. Iron has a mass number of 56, so it falls in the above zone. Carbon's mass number is 12 whereas lead's is 207. These two are away from the above zone.
      Thus between carbon and iron, iron has more binding energy per nucleon. So it is easier to take out a nucleon from carbon than iron. 
      Similarly, the binding energy per nucleon for lead is less than the iron. So it is easier to take out a nucleon from lead than iron.    





       5. Suppose we have 12 protons and 12 neutrons. We can assemble them to form either a 24Mg nucleus or two 12C nuclei. In which of the two cases more energy will be liberated?   

ANSWER: Due to the mass number, the binding energy per nucleon (say X) for Mg will be more than that for carbon (say Y). So the binding energy for Mg will be 24X. The binding energy of a carbon nucleus =12Y. For two carbon nuclei, total binding energy =24Y. 
          Since X > Y, →24X > 24Y. So one Mg nucleus has more binding energy than two C nuclei. Mg nucleus will release more energy.





       6. What is the difference between cathode rays and beta rays? When the two are traveling in space, can you make out which is the cathode ray and which is the beta ray?     

ANSWER: Both are formed with electrons but their origin is different. Cathode rays are formed in a cathode tube by accelerating the thermal electrons with a high potential difference. Beta rays are formed due to the disintegration of nuclei where neutrons convert into protons, emitting electrons.  
        Some electrons in a beta ray have high energy of the order of MeV that has some penetration power. Cathode rays have relatively low energy electrons that depend upon the potential difference applied across the cathode tube. They may be recognized by testing their energies in space.   





       7. If the nucleons of a nucleus are separated from each other, the total mass is increased. Where does the mass come from?   

ANSWER: Mass is a form of energy and they are related by E =mc². When the nucleons of a nucleus are separated, energy equal to the binding energy is required to be given to the nucleons. This energy is converted into mass, which is why the total mass is increased.    





       8. In beta decay, an electron (or a positron) is emitted by a nucleus. Does the remaining atom get oppositely charged?   

ANSWER: Suppose an electron is emitted in beta decay, the number of protons in the nucleus increases by one forming a new element. So the new atom requires one more electron in its orbit to remain electrically neutral. Since the orbiting electrons are unchanged, the remaining atom becomes an ion and is oppositely charged.    





       9. When a boron nucleus (105B) is bombarded by a neutron, an α-particle is emitted. Which nucleus will be formed as a result?   

ANSWER: The boron nucleus has 5 protons and 5 neutrons. When it is bombarded by a neutron, it emits an α-particle. An α-particle has two protons and two neutrons. So with the emission of an α-particle, two protons are reduced in the nucleus. There remains only 3 protons. So the new atomic number of the atom is 3 now, thus forming a Li atom.    





       10. Does a nucleus lose mass when it suffers gamma decay?   

ANSWER: No. The nucleons inside a nucleus move in discrete quantum states with different energies. In the ground state, the nucleons have minimum energy. They require very high energy, of the order of MeV's to go to higher excited states which is very difficult to provide. But in radioactive decay with α-particle or ß-particles, the newly formed daughter nucleus is generally in one of the excited states. The nucleons in the excited state eventually come to the ground state by releasing a photon (or photons) of electromagnetic radiation (similar to the process in a hydrogen atom when an electron jumps down to a lower energy state). These emitted photons by a nucleus have very high energy and are called gamma radiation and the process is gamma decay. As we have seen that gamma decay is only due to the change in energy state of the nucleus, no change of mass is involved. So the nucleus does not lose mass in a gamma decay.   





       11. In a typical fission reaction, the nucleus is split into two middle-weight nuclei of unequal masses. Which of the two (heavier or lighter) has greater kinetic energy? Greater linear momentum?    

ANSWER: In the given situation we consider only two unequal split masses. We assume that the original nucleus is at rest i.e. with zero momentum. From the conservation principle of momentum, after fission, total momentum should also be zero. Thus both fragments will have equal linear momentum but opposite in direction. 
      The relation between momentum and kinetic energy is given as, 
K.E. =½mv² =½(mv)²/m =p²/2m.  
        Since p is the same, the fragment having a lesser mass will have greater kinetic energy.      





       12. If three helium nuclei combine to form a carbon nucleus, energy is liberated. Why can't helium nuclei combine on their own and minimize energy?   

ANSWER: A helium nucleus contains two protons and two neutrons, it is positively charged. The nucleus is bound together due to attractive close-range nuclear force among the nucleons. The range of this force is very very short and decreases rapidly with distance. The positively charged helium nuclei repel each other with the electrostatic force which is a long-range force. So this repulsion from a distance will never let the helium nuclei come so near to each other where close-range attractive nuclear force is appreciable. Thus they are never able to combine on their own to form a carbon nucleus and minimize energy.  
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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"

Click here for "Questions for Short Answers"


Click here for "OBJECTIVE-II"

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