Bihar Board - Class 12 Physics - Chapter 13: Nuclei Long Answer Question

1. (a) What are isotopes? Give examples.

(b) What are isobars?

Answer:
(a) Isotopes of an element are the atoms of the element which have the same atomic number but different atomic weights. For example 1H1 , 1H2 , 1H3 are the isotopes of hydrogen. As isotopes of an element have the same atomic number, they contain the same number of protons and the same number of electrons. But as their atomic weights are different they contain different numbers of neutrons. Isotopes of an element have identical chemical properties. Their physical properties, however, differ. All the known elements have one or more isotopes. The relative abundance of different isotopes differs from element to element.

(b) Isobars are the atoms of different elements which have the same atomic weight, but different atomic numbers. Isobars contain different numbers of protons, different numbers of electrons and also different numbers of neutrons. Only the total number of nucleons in them is the same.

For example: 11Na22 and 10Ne22 are isobars. Similarly, 20Ca40 and 18Ar40 are isobars 17C137 and 16S37 are also isobars. The chemical properties of isobars are widely different. Their physical properties may be identical. Isobars occupy different places in the periodic table.

2. What is alpha decay, beta decay and gamma decay?

Answer:

During alpha decay, an alpha particle is emitted resulting in a decrease of mass number by 4 and atomic number by 2.

92U238 → 2He4 + 90Th234

During beta decay, a neutron of the nucleus disintegrates to give rise to proton, electron and antineutrino.

0n1 → -1p1 + -1e0 +

Reaction for emission of beta particles results in an increase of atomic number by 1 whereas the mass number remains constant.

90Th234 → -10 + 91Pa234

Gamma decay usually follows alpha decay. During alpha particle emission, the nucleus is left in an excited state.

To return to normal stage, it emits a single γ-ray of large energy or γ-rays are emitted in steps. However, during γ-decay, atomic number and mass number remain the same.

3. Define the term half life period and decay constant of a radioactive substance. Write their SI unit. Establish a relation between them.
Answer:

Half life period (T):  It is the time during which the number of atoms of a radioactive material reduces to half of the original number.

Decay constant (λ): Decay constant of a radioactive element is the time after which the number of radioactive atoms reduces to 1e times the original number of atoms in the sample.

Relation between T and λ:

Half life period. It is the time during which the number of atoms of a radioactive material reduces to half of the original number.
Let N0 = number of atoms at t = 0 (at the start of the observation)
N = number of atoms after time t
So,                                  N = N0e-λt ..........................(1)
where λ is constant called disintegration constant
Let T = half life period
So, when t = T, N = N0/2.
Substituting in Eq.(1), we have

                              N02 = N0e-t

                                        eλt = 2
                                  λT = loge2 = 2.303 log102  = 0.693
or                                         T = 0.693

4. What is nuclear fission? Give an example to illustrate it. What is the importance of the fission phenomenon?

Answer:
Nuclear fission: A process in which a heavy nucleus disintegrates into two lighter nuclei of nearly the same masses is called nuclear fission.
e.g. When slow neutron is bombarded on a heavy nucleus of 92U235 yielding two daughter nuclei Ba and Kr and tremendous amount of energy, the nuclear reaction can be represented as:
92U235 + 0n1 → 92U236 → 56Ba141 + 36Kr92 + 30n1 + ∆Q

Importance of nuclear fission:
1. Controlled nuclear fission is used in number of yields e.g.
(а) to prepare isotopes.
(b) to generate power for propulsion of ships, submarines and aircrafts.
(c) to produce plutonium for explosive purposes.

2. Uncontrolled nuclear fission is used in atomic bombs.

5. Distinguish between nuclear fission and nuclear fusion.

Answer:
Distinction between Nuclear fission and Nuclear fusion:
Nuclear fission

• A bigger nucleus is split into two or more smaller nuclei.

• It produces a lot of energy.

• Nuclear reactions can be controlled.

• It is the principle of an atom or fission bomb.

Nuclear fusion

• Two light nuclei combine to form a heavier nucleus.

• It also produces huge energy.

• Nuclear reactions can be controlled.

• It is the principle of hydrogen or fusion bombs.

6. Draw a plot of the binding energy per nucleon as a function of mass number for a large number of nuclei. Explain the energy release in the process of nuclear fission from the above plot. Write a typical reaction in which a large amount of energy is released in the process of nuclear fission.

Or

Draw a graph showing the variation of binding energy per nucleon verses the mass number. Explain with the help of this graph the release of energy in the process of nuclear fission and fusion.

Answer:

Plot of binding energy per nucleon is shown in fig.  

From the graph we find that

1. The binding energy per nucleon increases gradually from mass number A = 20 to mass number A = 40.

2. The curve is almost flat between mass number 40 and 120. This means that the variation in binding energy per nucleon in the range is small (about 10%). The average binding energy per nucleon in this region is about 8.5 MeV. It is maximum for iron (26Fe59 ) and has a value of 8.8 MeV.

3. The binding energy per nucleon decreases slowly and continuously from A = 120 to A = 240. It reaches a value of 7.6 MeV at A = 238. Thus we find that if any nucleon with A = 240 breaks into two nuclei, nucleons get more lightly bound, so energy would be released in the process. This process is called nuclear fission.

4. When two light nuclei (A < 10) are joined to form a heavier nucleus, the binding per nucleon of the fused heavier nuclei is more than the binding energy per nucleon of the lighter nuclei. Hence we find that the final system is more tightly bound than the initial system, and the energy released in this process is called nuclear fusion.

A typical nuclear fission reaction is

92U235 + 0n1 → 92U236   → 56Ba144 + 36Kr92 + 30n1 + 200 MeV

7. What is radioactivity? What is the difference between natural and induced radioactivities?

Answer:
Radioactivity:  The phenomenon of spontaneous disintegration of the nucleus of an atom with the emission of some radiation is called radioactivity. There are a number of heavy elements occurring in nature whose nuclei are unstable and undergo spontaneous disintegration with emission of some radiation. The rate of emission or intensity of radiation is not influenced by any external agency such as the temperature or pressure. The substances having this property are called radioactive substances.

Natural and induced (or artificial) radioactivities: The radioactivity exhibited by some naturally occurring elements is called natural radioactivity. All elements with atomic number greater than 82 are radioactive. It is, however, possible to induce radioactivity in the elements with atomic number less than 83 by artificial means. This type of radioactivity is called induced or artificial radioactivity.

8. Explain properties of α-rays.

Answer:

Properties of α-rays:

1. The α-rays are shot out from the radioactive material with large velocities ranging from 1.4 x 107 to 2.3 x 107ms-1.

2. They produce ionization in the gas through which they pass. The ionizing power is 100 times greater than that of ß-rays and 10,000 times greater than that of γ-rays.

3. They affect a photographic plate. The effect is very-very feeble.

4. They produce fluorescence in substances like zinc sulfide, barium platinocyanide etc.

5. The α-rays are scattered when they pass through thin sheets of mica, gold foil etc. The angle of divergence of α-particles from its straight path is 2 to 3 degrees. Geiger and Marsaden found that a few particles, sometimes, were deflected by more than 20°. This was explained by Rutherford to be due to the repulsion between α-particles and the positively charged nucleus of the atom.

6. The α-rays are deflected by electric and magnetic fields showing that they are charged particles. 

7. They produce a heating effect. A quantity of radium always maintains itself at a temperature higher than that of the surroundings. The evolution of heat is due to the stoppage of α, ß and γ rays by the radioactive substance.

8. The body suffers incurable burns when exposed to α-rays.

9. Define the terms nucleus, nucleons, atomic number, mass number, nuclide, isotopes, isobars, isotones and isomers.
Answer:
Nucleus: A nucleus consists of protons and neutrons and the size of nucleus is about 10-14 m. The protons and neutrons inside the nucleus go on interchanging to each other and hence called nucleons (i.e. protons or neutrons).

Nucleons: Protons and neutrons inside the nucleus of an atom are called nucleons.

Atomic number (Z): The number of protons in the nucleus is called the atomic number of the element.

Mass number (A): Total number of nucleons in the nucleus is called mass number i.e. A = Z + N, so number of neutrons in the nucleus N = A - Z.

Nuclide: A nuclide is a specific nucleus of an atom characterized by its atomic number Z and mass number A Symbolically, nuclide is represented by XZA.

Isotopes: The atoms of an element which have the same atomic number but different mass number are called isotopes, e.g. 8O16, 8O17 ,8O18 are three isotopes of oxygen and 17Cl35, 17Cl37 are two isotopes of chlorine.

Isobars: The atoms having the same mass number but different atomic numbers are called isobars e g. 18Ar40 , 20Ca40 and 1H3,2H3. Isobars have the same numbers of nucleons.

Isotones: Atoms whose nuclei have the same number of neutrons are called isotones e.g.17Cl37 and 19Cl39 .

Isomers: The nuclei have the same atomic number and same mass number but in different energy states are called isomers e.g. a nucleus in its ground state and the identical nucleus in metastable excited state are isomers.

10. Write a note on the structure of the nucleus.

Answer:

Structure of nucleus: Rutherford's experiments on the scattering of α-particles by atoms led to the discovery of a positively charged heavy central core, called nucleus, of radius of the order of 10-15 m.

1. The entire positive charge and almost the entire mass of the atom is concentrated in the nucleus.

2. Nucleus contains protons and neutrons called nucleons. A proton carries a unit positive charge and mass 1836 times that of an electron. The neutron is electrically neutral and has mass 1836.6 times that of an electron. The number of protons in the nucleus is called atomic number (Z) whereas the total number of neutrons and protons is called mass number (A).

3. Negatively charged electrons round the nucleus revolve in various orbits. The negative charge on the electron is of the same magnitude as the positive charge on the proton. The number of electrons revolving around the nucleus is equal to that of protons so that an atom is normally electrically neutral.

11.Describe the nucleus as a source of nuclear energy.

Answer:
Nucleus as a source of Nuclear Energy:
Binding energy curve shows that average binding energy is 8.5 MeV per nucleon for moderate nuclei with mass number 40 to 120. It is less than this for lighter nuclei with A < 40 and also for heavy nuclei with A > 120. It means that light and heavy nuclei are less tightly bound. Whenever nuclei of less average binding energy per nucleon are converted into those of more average binding energy, some mass is converted into energy.

From this situation, it is expected that energy will be evolved if heavy nuclei be split into moderate nuclei or light nuclei be joined (fused) to form a less light nuclei. The former process is known as nuclear fission and the latter as nuclear fusion. Both these processes become source of nuclear energy.

12. Explain properties of neutrons.

Answer:

Properties of neutrons.

1. Neutron is an elementary particle having mass equal to 1.6748 x 10-27 kg.

2. It is an uncharged particle and hence the electric and magnetic fields have no influence on it.

3. It possesses very high penetrating power due to its neutral character.

4. It possesses very low ionizing power (again due to its neutral character).

5. The neutrons can be slowed down by passing them through heavy water, paraffin wax, graphite etc. This happens due to the scattering of the neutrons. The scatterers are commonly known as moderators.

6. The slow neutrons, also known as thermal neutrons, are found to be more efficient in causing nuclear reactions.

7. Neutron is a stable particle within the nucleus. However, outside the nucleus, the neutron is an unstable particle. Its half life period is about 12 minutes. It decays according to the following scheme:
                             0n1 → 1H1  + -1e0  + 
   where   is called antineutrino.

13. Describe forces which keep nucleons bound together giving their definitions, properties and theory.

Answer:
The forces that keep the nucleons bound together in a nucleus are called nuclear forces.

Nuclear force: We know that inside the nucleus there are protons and neutrons and the Coulomb's force of repulsion is about 1036 times as large as the gravitational force of attraction between two protons. Hence the nucleus should not be stable, but we find that the nucleus is very stable, it means that there must be a third type of force which is stronger than the coulomb's force and exists in the nucleus which is responsible for binding the nucleons together in the nucleus. This force is called nuclear force and it is about 100 times stronger than the coulomb's force.

Properties.

1. They are strong attractive forces and exist between two protons, between two neutrons and between a proton and a neutron.

2. They are charge independent. Force between two protons = force between two neutrons = force between a proton and neutron.

3. They are spin dependent. It is more between nucleons having spin in the same direction and less between those having spin in opposite directions.

4. They are short range forces. It is effective only upto a distance of 10 x 10-15 m (10 fermi) and zero beyond it. Hence it is not extended from one nucleon to all nucleons of the nucleus.

5. They vary with distance. They start acting only when the distance between nucleons becomes 10 fermi. As distance decreases, force increases. Increase is slow upto 5 fermi and then rapid. Force is maximum at distance 15 fermi.

At lesser distances, repulsive forces start acting, decreasing the attractive force.

14. Explain properties of ß-rays.

Answer:

Properties of ß-rays:

1. ß-rays are shot out from radioactive elements with very high velocities ranging from 1% to 99% of the velocity of light. The velocity of all ß-particles given out by an element is not the same.

2. They produce ionization in air but the number of ions produced is very less than those of α-rays. Although their velocity is very large they possess a comparatively small mass than that of α-particles and hence they have small kinetic energy. As ß-particles are slowed down by collision with the atoms of the gas and change their path, their tracks in a Wilson Cloud Chamber are scattered and not continuous as those of α-particles.

3. They affect a photographic plate and their effect is greater than those of α-rays.

4. ß-rays produce fluorescence in barium, platinocyanide, calcium, tungsten, willemite etc.

5. Because of their small mass, they can penetrate through large thickness of matter, e.g They can easily pass through 1 cm of thick aluminum sheet.

6. They are more easily scattered when they pass through matter, because their mass is very small as compared to the mass of the atomic nuclei.

15. Explain properties of γ-rays.

Answer:

Properties of γ-rays:

1. The velocity of γ-rays is the same as that of light i.e. 3 x 108 ms-1.

2. They produce ionization in gasses through which they pass but their effect is very small as compared to that of α-rays and ß-rays. This is due to the fact that their mass is very small as compared to that of α and ß-ray particles.

3. They affect photographic plates and their effect is greater than those for ß-rays.

4. They produce fluorescence in barium, platinocyanide, etc.

5. They are more penetrating than even ß-rays and can pass very easily through 30 cm thickness of iron.

6. They are diffracted from crystals in a way similar to X-ray diffraction.

7. They are not affected by electric and magnetic fields. This shows that they are neutral particles; further experiments have shown that they are similar to e.m. rays.

8. γ-rays can be absorbed by the matter.

16. What is the rate of decay? What are the units of measuring radioactivity?

Answer:
Rate of Decay (R):   It is equal to the number of radioactive disintegrations in the sample taking place per second. Mathematically, it is represented as:
                                        R (t) = dNdt = λN (t) ....................(1)

Unit of measuring radioactivity
Radioactivity is measured by the number of radioactive nuclei that decay per second. The two units of radioactivity are curie (ci) and Rutherford (rd).
(i) Curie:  It is the radioactivity of 1 gram of radium. One gram of radium gives only 3.7 x 1010disintegrations per second. Therefore, the radioactivity of a sample is said to be 1 curie if it undergoes 3.7 x 1010 disintegrations per second.
∴ 1 ci = 3.7 x  1010 disintegrations, and 1µ ci= 3.7 x  104 disintegrations.

(ii) Rutherford (rd): The radioactivity of a material is said to be 1 Rutherford if it undergoes  106 disintegrations per second. Thus
                                        1 rd =  106 disintegrations
∴ 1 µ ci = 3.7 x  104 rd and 1 m ci = 37 rd.

17. What do you mean by nuclear reaction? What quantities are conserved in nuclear reaction? 

Answer:
Nuclear Reaction:
The conversion of the nucleus of an element into a nucleus of another element is called a nuclear reaction. This is generally caused by bombarding the target nucleus by high energy particles.

For example, if an incident projectile ‘a’ hits the target nucleus X, a nuclear reaction takes place and as a result there is a new nucleus Y and an outgoing particle ‘b’ are produced.
i.e.                                               a + X → Y + b
In short form, this reaction can be written as X (a,b) Y.
In 1919, Rutherford observed that when α-particles, from a polonium source were made to hit nitrogen atoms, protons were given off in the reaction. The nuclear reaction for this process can be written as
7N14 + 2He4 → 8O17 + H1  The above reaction can also be written as 7N14 (α,p) 8O17.
Following quantities remain conserved during a nuclear reaction.

1. Conservation of charge. Total charge of the reactant is conserved.

2. Conservation of nucleons. Total number of nucleons before and after the reaction remains constant.

3.  Mass and energy conservation. In a nuclear reaction mass and energy are not separately conserved. However, their total is always conserved i.e. the energy equivalent of mass is liberated as can be understood in the Q-value of the nuclear reactions.

4. Conservation of linear momentum. It is a fundamental law and is always conserved in nuclear reactions also.

5. Conservation of angular momentum. Total angular momentum J is composed of orbital angular momentum L and spin angular momentum S. Vector sum of the total angular momentum is conserved in a nuclear reaction.

18. Explain nuclear fusion. What are the conditions for fusion?

Answer:
Nuclear fusion:

 Nuclear fusion is a process in which lighter nuclei (like 1H1) are fused together into heavier atoms (like 2He4), with the release of enormous amounts of energy. The energy thus released is known as thermonuclear energy and the reaction is called thermonuclear reaction. The cause of energy is again mass defect. Nuclear fusion takes place at very high temperature and very high density.
e.g. two deuterons can fuse together to form a medium nucleus and release energy of about 24 MeV.
i.e., 1H2 +1H2→ 2He4 + 24 MeV.
Some other examples of such reactions are
1H1 + 1H1 → 1H2 + 1e0 + 0.42 MeV
41H1 → 2He4 + 2 +1e0 + 26.7 MeV
1H3 + 1H2 → 2He4 + 0n1  + 17.6 MeV
3Li7 + 1H1 → 2He4 + 2He4 + 17.3 MeV.
Nuclear fusion reactions take place in the presence of very high temperatures (about 107 K), so they are called thermonuclear reactions. All these reactions are exergonic and release huge energies. The energy that comes from the conversion of mass of the final stage nucleus formed as a result of fusion is always less than that of the individual light nuclei.
The temperature of the order of 107 K is very difficult to obtain. The mechanism involved for producing high temperature is a self-sustained fission explosion. When an atom bomb containing U235 explodes, very high temperature ( ≃ 107 K) is produced. Thus an atomic explosion acts as a trigger and releases a tremendous amount of energy.

Conditions for Fusion:
(1) Either the reacting nuclei should be given a large amount of kinetic energy to overcome the mutual repulsion between them.
(2) Or a very high temperature should be produced. Such high temperatures exist in the territory of stars. Therefore, thermal fission is possible in stars.

19. (i) Write three characteristic properties of nuclear force.

(ii) Draw a plot of potential energy of a pair of nucleons as a function of their separation. Write two important conclusions that can be drawn from the graph.

Answer:

(i) Characteristic Properties of Nuclear Force

(a) Nuclear force acts between a pair of neutrons, a pair of protons and also between a neutron-proton pair, with the same strength. This shows that nuclear forces are independent of charge.

(b) The nuclear forces are dependent on spin or angular momentum of nuclei.

(c) Nuclear forces are non-central forces. This shows that the distribution of nucleons in a nucleus is not spherically symmetric. From the plot, it is concluded that

(ii)

(a) The potential energy is minimum at a distance r0 (=0.8fm) which means that the force is attractive for distances larger than 0.8 fm and repulsive for the distance less than 0.8 fm between the nucleons.

(b) Nuclear forces are negligible when the distance between the nucleons is more than 10 fm.

20. How many electrons, protons and neutrons are there in 12 g of 6C12  and in 14 g of 6C14 ?

Answer:

12 g of 6C12   has number of atoms = 6 x 1023

∴ the number of electrons in 12 g of 6C12   

                                   = 6 x 6 x 1023 = 36 x1023

The number of protons in 12 g of 6C12   = 36 x 1023

The number of neutrons in 12 g of6C12  = (A - Z) x 6 x 1023 = 6 x 6 x1023 = 36 x 1023

Similarly

No. of electrons in 14 g of 6C14 = 36 x 1023

No. of protons in 14 g of 6C14 = 36 x1023

No. of neutrons in 14 g of 6C14 = (A - Z) x 6 x 1023

                                      = (14 - 6) x 6 x1023

                                       = 48 x1023.

21. Write down the postulates of the Bohr atom model.

Answer: 

Postulates of the Bohr atom model:

(1) The electron in an atom moves around the nucleus in circular orbits under the influence of Coulomb electrostatic force of attraction. This force gives necessary centripetal force for the electron to undergo circular motion.

(2) Electrons in an atom revolve around the nucleus only in certain discrete orbits which do not radiate electromagnetic energy called stationary orbits. The angular momentum of the electrons in these stable orbits are quantized ie., angular momentum equal to integral multiple of h/2π

                                                            l  = nh / 2π

This is Angular momentum Quantization condition

(3) Energy of orbits are not continuous but only discrete i.e., Quantization of energy.

(4) An electron can jump from one orbit to another orbit by absorbing or emitting a photon whose energy is equal to the difference in energy (∆E) between the two orbital levels.

                                             ΔE =Efinal – Einitial = hυ = hc / λ

 υ = Frequency; h = Planck’s constant

22. Explain giving necessary reaction, how energy is released during:
(i) fission
(ii) fusion

Answer:
(i) Nuclear Fission: The phenomenon of splitting of heavy nuclei (mass number > 120) into smaller nuclei of nearly equal masses is known as nuclear fission. In nuclear fission, the sum of the masses of the product is less than the sum of masses of the reactants. This difference of mass gets converted into energy E = me and hence a sample amount of energy is released in a nuclear fission.
e.g., 92U235 + 01n → 56Ba141 + 36Kr92 + 3 0n1+ Q
Masses of reactant = 235.0439 amu + 1.0087 amu
                              = 236.0526 amu
Masses of product = 140.9139 + 91.8973 + 3.0261
                              = 235.8373 amu
Mass defect = 236.0526 -235.8373
                              = 0.2153 amu
∵ 1 amu = 931MeV
⇒ Energy released = 0.2153 x 931
⇒ 200 MeV nearly

(ii) Nuclear Fusion: The phenomenon of conversion of two lighter nuclei into a single heavy nucleus is called.nuclear fusion. Since the mass of the heavier product nucleus is less than the sum of masses of reactant nuclei and therefore a certain mass defect occurs which converts into energy as per Einstein’s mass-energy relation. Thus, energy is released during nuclear fusion.
e.g., 1H1 + 1H1 → 1H2 + e+ + v + 0.42 MeV
Also,1H2 + 1H2 →1H3 + 1H1 + 4.03 MeV

23. Define ‘electron volt’ and ‘Atomic mass unit”. Find out the energy equivalent to mass of a proton in a joule.

Answer:
Electron volt:
The energy acquired by an electron when it is being accelerated by a potential difference of 1 volt is called ‘electron volt’.
1 electron volt = 1.6 x 10-19J.

Atomic mass unit:
An atomic mass unit is defined as (112) of the mass of 1 atom of carbon – 12.
1 atomic mass unit = 1.66 x 10-27 kg
(1 a.m.u. or only 1u)
The mass of proton = 1.673 x 10-27 x (3 x 108 )2
= 15.05 x 10-11 J
= 1.505 x 10-10J
∴ The energy equivalent mass of 1 proton is 1.505 x 10-10J

24. Give reasons for :
(a) Lighter elements are better moderators for a nuclear reactor than heavier elements.
(b) In a natural uranium reactor, heavy water is preferred as compared to ordinary water.
(c) Cadmium rods are provided in a reactor.

Answer:
(a) A moderator slows down fast neutrons released in a nuclear reactor. The basic principle of mechanics is that the energy transfer in a collision is the maximum when the colliding particles have equal masses. As lighter elements have mass close to that of neutrons, lighter elements are better moderators than heavier elements.

(b) Ordinary water has hydrogen nuclei (11H) which have greater absorption capture for neutrons; so ordinary water will absorb neutrons rather than slowing them; on the other hand, the heavy hydrogen nuclei (12H) have negligible absorption capture for neutrons, so they share energy with neutrons and neutrons are slowed down.

(c) Cadmium has high absorption capture for neutrons; so cadmium rods are used to absorb extra neutrons; so nuclear fission in a nuclear reactor is controlled; therefore cadmium rods are called control rods.

25. What are cathode rays? Write the properties of cathode rays.

Answer :

Cathode rays are streams of electrons emitting from cathode in a Coolidge tube at a pressure of around 0.01 mm of Hg.

Properties of cathode rays:

(1) Cathode rays possess energy and momentum

(2) They travel in a straight line

(3) They are deflected by electric and magnetic fields

(4) They affect photographic plates

(5) They produce fluorescence when they fall on certain crystals and minerals

(6) They ionize the gas through which they pass

(7) They produce heat, when they fall on matter

(8) They are negatively charged particles nothing but electrons

(9) When the cathode rays fall on a material of high atomic weight, X-rays are produced.