OBJECTIVE-II
1. As the mass number A increases, which of the following quantities related to a nucleus do not change?
(a) mass
(b) volume
(c) density
(d) binding energy.
ANSWER: (c).
EXPLANATION: With the increase in mass number A, the number of nucleons increases. Thus mass and volume both increase. Also, the binding energy of the nucleus increases because, the more the number of nucleons, the more energy is required for disintegrating the nucleus in its constituents. Hence options (a), (b), and (d) are incorrect.
Let us see what happens with density. Suppose the average mass of a nucleon =m, then the mass of a nucleus =mA.
The radius of a nucleus, R =RₒA1/3
where Rₒ =1.1 fm.
The volume of a nucleus,
V =4πR³/3 =4πRₒ³A/3
Hence the density of a nucleus,
D =mass/volume
=3mA/4πRₒ³A
=3m/4πRₒ³.
This expression for the density is a constant.
Hence option (c) is correct.
2. The heavier nuclei tend to have a larger N/Z ratio because
(a) A neutron is heavier than a proton
(b) A neutron is an unstable particle
(c) A neutron does not exert electric repulsion
(d) Coulomb forces have a larger range compared to the nuclear forces.
ANSWER: (c), (d).
EXPLANATION: In heavier nuclei, the number of protons is more. They exert repulsive Coulomb force on each other which is a long-range force. To stabilize a heavier nucleus, neutrons play a vital role as they have no electrostatic charge, they do not repel other nucleons and they only exert attractive close-range nuclear force. It resists the stronger Coulomb force in heavier nuclei and helps the nucleus remain together, so the N/Z ratio is higher.
A neutron is marginally heavier than a proton but it has nothing to do with the N/Z ratio. A neutron is not an unstable particle. Options (a) and (b) are incorrect.
Options (c) and (d) are correct.
3. A free neutron decays to a proton but a free proton does not decay to a neutron. This is because
(a) neutron is a composite particle made of a proton and an electron whereas a proton is a fundamental particle.
(b) neutron is an uncharged particle whereas a proton is a charged particle
(c) neutron has a larger rest mass than the proton
(d) Weak forces can operate in a neutron but not in a proton.
ANSWER: (c).
EXPLANATION: A free proton can not decay into a neutron because a neutron has a larger rest mass than the proton. If this process is possible then the Q-value will be negative which is not acceptable and possible. Q-value is the difference in mass of the sum of the rest masses of constituents and the rest mass of the final product.
Options (a) and (d) are incorrect, while option (b) is not a reason that a free proton does not decay to a neutron. Only option (c) is correct.
4. Consider a sample of a pure beta-active material.
(a) All the beta particles emitted have the same energy
(b) The beta particles originally exist inside the nucleus and are ejected at the time of decay.
(c) The antineutrino emitted in a beta decay has zero mass and hence zero momentum.
(d) The active nucleus changes to one of its isobars after the beta decay.
ANSWER: (d).
EXPLANATION: All beta particles do not have the same kinetic energy because this energy is shared by the beta particle and the antineutrino/neutrino emitted during the decay. Depending upon the proportion of sharing, the kinetic energy of beta particles varies. Option (a) is wrong.
Beta particles do not originally exist inside a nucleus. They are formed and emitted when inside an active nucleus either a neutron decays into a proton and electron or a proton decays into a neutron and a positron. Thus the resulting nucleus is an isobar of the previous one. Option (b) is wrong but option (d) is correct. Antineutrino emitted in a beta decay have zero mass but possess momentum. Option (c) is incorrect.
5. In which of the following decays the element does not change?
(a) α-decay
(b) ß⁺-decay
(c) ß⁻-decay
(d) 𝛾-decay
ANSWER: (d).
EXPLANATION: Only in a gamma decay the element does not change because the emitted gamma rays are not charged particles but electromagnetic radiation which is a result of the newly formed nucleus coming down to the ground state of energy.
Other given particles are charged particles and their emission changes the atomic number of the nucleus. Since the atomic number decides the element, with the emission of these charged particles the element changes.
Option (d) is correct.
6. In which of the following decays does the atomic number decrease?
(a) α-decay
(b) ß⁺-decay
(c) ß⁻-decay
(d) 𝛾-decay.
ANSWER: (a), (b).
EXPLANATION: A decrease in atomic number means a decrease in the number of protons in a nucleus. In an α-decay two protons and two neutrons are emitted from a nucleus. So the atomic number decreases by two.
In a beta-plus decay, a proton is converted into a neutron and a positron. The resulting neutron remains in the nucleus while the positron is emitted. Thus the nucleus now has one proton less resulting in a decrease in atomic number.
In a beta-minus decay, a neutron is converted into a proton and an electron. The electron is emitted as a beta-minus ray. Due to the resulting proton, the number of protons in the nucleus increases i.e. the atomic number increases.
Since gamma rays are electromagnetic radiations not charged particles, the atomic number of the element remains the same.
Clearly, options (a) and (b) are correct only.
7. Magnetic field does not cause deflection in
(a) α-rays
(b) beta-plus rays
(c) beta-minus rays
(d) gamma rays.
ANSWER: (d).
EXPLANATION: A magnetic field causes a deflection in a moving charged particle. The α-rays, beta-plus rays, and beta-minus rays are charged particles, hence they get deflected by a magnetic field.
Gamma rays are electromagnetic radiations not charged particles, so they are not deflected by a magnetic field.
Option (d) is correct.
8. Which of the following are electromagnetic waves?
(a) α-rays
(b) beta-plus rays
(c) beta-minus rays
(d) gamma rays.
ANSWER: (d).
EXPLANATION: α-rays are helium nuclei, beta-plus rays are positrons (a particle similar to an electron but with opposite charge) and beta-minus rays are electrons. All these three are particles with a certain mass. Only gamma rays are electromagnetic waves.
Option (d) is correct.
9. Two lithium nuclei in a lithium vapor at room temperature do not combine to form a carbon nucleus because
(a) A lithium nucleus is more tightly bound than a carbon nucleus
(b) A carbon nucleus is an unstable particle
(c) It is not energetically favorable
(d) Coulomb repulsion does not allow the nuclei to come very close.
ANSWER: (d).
EXPLANATION: As we know most of an atom is hollow with a heavy nucleus with a positive charge at the center. So these positively charged nuclei repel each other with Coulomb force which is a long-range force. Nuclei can combine together only if they are close enough (separations of the order of a few fm) so that close-range attractive nuclear forces are effective. As in the given case, the lithium vapor is at room temperature. If two randomly moving lithium atoms hit each other they will get orbiting electrons in one atom repelling other's with Coulomb force because they do not form a covalent bond. Even if the nuclei may overcome the orbiting electrons, both nuclei will repel each other with Coulomb force. So they can not come close enough to get the attractive nuclear force significant in magnitude.
The first three options are incorrect, option (d) is correct.
10. For nuclei with A > 100,
(a) The binding energy of the nucleus decreases on average as A increases
(b) The binding energy per nucleon decreases on average as A increases
(c) If the nucleus breaks into two roughly equal parts, energy is released
(d) If two nuclei fuse to form a bigger nucleus, energy is released.
ANSWER: (b), (c).
EXPLANATION: With increasing A, the number of nucleons increases and hence the binding energy of the nucleus increases. Option (a) is incorrect.
For nuclei A > 100, binding energy per nucleon decreases on average as A increases. It is due to the fact that inner nucleons are surrounded fully and their interactions with other nucleons reach nearly maximum. But with an increase in A, the surface area of the nucleus also increases. Surface nucleons are not fully surrounded and hence their interactions with other nucleons are not saturated. Due to this, the binding energy per nucleon decreases on average as A increases. Option (b) is correct.
When a nucleus with A > 100 breaks into two roughly equal parts, the binding energy per nucleon of these parts will be more than the parent nucleus. So if we mathematically add the binding energy of these two daughter nuclei, the sum will be more than the binding energy of the parent nucleus. Thus in this process, energy is released. Option (c) is correct.
If two nuclei with A > 100 fuse together, the resulting nucleus will have binding energy per nucleon less than the parent nuclei. Thus the binding energy of the resulting nucleus will be less than the sum of the binding energy of two parent nuclei. So in this process, energy will not be released but it will require energy. Option (d) is incorrect.
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Links to the Chapters
Links to the Chapters
CHAPTER- 46- The Nucleus
CHAPTER- 45- Semiconductors and Semiconductor Devices
CHAPTER- 44- X-raysCHAPTER- 43- Bohr's Model and Physics of AtomCHAPTER- 42- Photoelectric Effect and Wave-Particle DualityCHAPTER- 41- Electric Current Through Gases
CHAPTER- 40- Electromagnetic WavesCHAPTER- 39- Alternating CurrentCHAPTER- 38- Electromagnetic Induction
CHAPTER- 37- Magnetic Properties of MatterCHAPTER- 36- Permanent Magnets
CHAPTER- 35- Magnetic Field due to a Current
CHAPTER- 34- Magnetic Field
CHAPTER- 33- Thermal and Chemical Effects of Electric Current
CHAPTER- 46- The Nucleus
CHAPTER- 45- Semiconductors and Semiconductor Devices
CHAPTER- 44- X-rays
CHAPTER- 43- Bohr's Model and Physics of Atom
CHAPTER- 42- Photoelectric Effect and Wave-Particle Duality
CHAPTER- 41- Electric Current Through Gases
CHAPTER- 40- Electromagnetic Waves
CHAPTER- 39- Alternating Current
CHAPTER- 38- Electromagnetic Induction
CHAPTER- 37- Magnetic Properties of Matter
CHAPTER- 36- Permanent Magnets
CHAPTER- 35- Magnetic Field due to a Current
CHAPTER- 34- Magnetic Field
CHAPTER- 33- Thermal and Chemical Effects of Electric Current
CHAPTER- 32- Electric Current in ConductorsCHAPTER- 31- CapacitorsCHAPTER- 30- Gauss's Law
CHAPTER- 29- Electric Field and Potential
CHAPTER- 28- Heat Transfer
OBJECTIVE -I
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- 21 - Speed of Light
CHAPTER- 20 - Dispersion and Spectra
CHAPTER- 19 - Optical Instruments
CHAPTER- 18 - Geometrical Optics
CHAPTER- 17 - Light Waves
CHAPTER- 16 - Sound Waves
CHAPTER- 15 - Wave Motion and Waves on a String
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- 32- Electric Current in Conductors
CHAPTER- 31- Capacitors
CHAPTER- 30- Gauss's Law
CHAPTER- 29- Electric Field and Potential
CHAPTER- 28- Heat Transfer
CHAPTER- 26-Laws of Thermodynamics
CHAPTER- 25-CALORIMETRY
Questions for Short Answer
OBJECTIVE-I
OBJECTIVE-II
CHAPTER- 24-Kinetic Theory of Gases
CHAPTER- 23 - Heat and Temperature
CHAPTER- 21 - Speed of Light
CHAPTER- 20 - Dispersion and Spectra
CHAPTER- 19 - Optical Instruments
CHAPTER- 18 - Geometrical Optics
CHAPTER- 17 - Light Waves
CHAPTER- 16 - Sound Waves
CHAPTER- 15 - Wave Motion and Waves on a String
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
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CHAPTER- 7 - Circular Motion
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CHAPTER- 6 - Friction
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CHAPTER- 6 - Friction
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CHAPTER- 5 - Newton's Laws of Motion
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Click here for → QUESTIONS FOR SHORT ANSWER
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Click here for → Newton's Laws of Motion - Objective -II
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Click here for → Newton's Laws of Motion-Exercises(Q. No. 1 to 12)
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"
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Click here for "The Forces" - OBJECTIVE-II
Click here for "The Forces" - Exercises
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CHAPTER- 3 - Kinematics - Rest and Motion
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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"
CHAPTER- 2 - "Physics and Mathematics"
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