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Modern Physics 10

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TARGET IIT   X PHYSICS   M 1- UNIVERSE IIT   ian’s PACE Education Pvt. Ltd. : Andheri/Dadar/Chembur /Than e/Churchgate/Neru l/Powai # 28 CHAPTER 5 MODERN PHYSICS NUCLEAR STRUCTURE (a) Composition The central core of an atom is called as nucleus. The nucleus of any atom of an element has two types of fundamental particles, i.e., protons and neutrons. Collectively all the particles found within the nucleus are called nucleons. (b) Charge Nucleus owes its positive charge due to protons. Among all the elements, the nuclear charge is minimum for the hydrogen and it is equal to the charge of 1 proton. Naturally occurring element whose nuclear charge is maximum is uranium and it is equal to the charge of 92 protons. The proton is a positively charged particle having a charge of + 1.6 10 -19 coulombs and mass kg. However, its mass is 1837 times greater than the mass of one electron. The neutron apparently has no electric charge, and its mass is slightly greater than the mass of one proton. (c) Representation of Nucleus Mass number (A): It represents total number of nucleons present within the nucleus, i.e., the number of protons and neutrons. It is also known as mass number or atomic weight.  Atomic number (Z): It represents total number of protons, within the nucleus of an atom. It is numerically equal to the number of electrons revolving around the nucleus. It is also known as atomic number or proton number. It controls the chemical and physical properties of an element. N represents total number of neutrons present in the nucleus of an atom. Thus, Mass number = Number of protons + Number of neutrons or A = Z + N If X is the symbol of some element, such that A is its mass number and Z is its atomic number then symbolically its nucleus is represented as Z X  A  For example, for oxygen A = 16 and Z = 8 and hence symbol for its nucleus is 8 O 16  It must be kept in mind that the superscript represents mass number and sub-script represents atomic number. (d) Mass of the nucleus It is expressed in terms of the unit called atomic mass unit (a.m.u)  Atomic mass unit: the mass of molecules, atoms, nucleus and atomic particles is measured in a unit called “atomic mass unit”. This is denoted by „a.m.u. One atomic mass unit is one- twelfth of the mass of a carbon atom. 1 a.m.u = 1.66 × 10 -24 gm (e) Size of nucleus Radius of nucleus is used to measure the size of the nucleus. The unit used for measuring the size of the nucleus is Fermi (F). 1 Fermi = m The radius of a nucleus is,    
Transcript
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TARGET IIT  – X PHYSICS  – M 1- UNIVERSE

IIT –  ian’s PACE Education Pvt. Ltd. : Andheri/Dadar/Chembur /Thane/Churchgate/Nerul/Powai # 28

CHAPTER – 5

MODERN PHYSICS

NUCLEAR STRUCTURE

(a) CompositionThe central core of an atom is called as nucleus. The nucleus of any atom of an element hastwo types of fundamental particles, i.e., protons and neutrons. Collectively all the particlesfound within the nucleus are called nucleons.

(b) ChargeNucleus owes its positive charge due to protons. Among all the elements, the nuclear chargeis minimum for the hydrogen and it is equal to the charge of 1 proton. Naturally occurringelement whose nuclear charge is maximum is uranium and it is equal to the charge of 92protons.

The proton is a positively charged particle having a charge of + 1.6 10-19 coulombs andmass kg. However, its mass is 1837 times greater than the mass of oneelectron.The neutron apparently has no electric charge, and its mass is slightly greater than the massof one proton.

(c) Representation of NucleusMass number (A): It represents total number of nucleons present within the nucleus, i.e.,the number of protons and neutrons. It is also known as mass number or atomic weight.

 Atomic number (Z): It represents total number of protons, within the nucleus of an atom. Itis numerically equal to the number of electrons revolving around the nucleus. It is also

known as atomic number or proton number. It controls the chemical and physicalproperties of an element.N represents total number of neutrons present in the nucleus of an atom.

Thus,Mass number = Number of protons + Number of neutrons or A = Z + N

If X is the symbol of some element, such that A is its mass number and Z is its atomicnumber then symbolically its nucleus is represented as ZX A  For example, for oxygen A = 16 and Z = 8 and hence symbol for its nucleus is 8O16 It must be kept in mind that the superscript represents mass number and sub-script

represents atomic number.

(d) Mass of the nucleusIt is expressed in terms of the unit called atomic mass unit (a.m.u)

 Atomic mass unit: the mass of molecules, atoms, nucleus and atomic particles is measuredin a unit called “atomic mass unit”. This is denoted by „a.m.u‟. One atomic mass unit is one-twelfth of the mass of a carbon

atom.1 a.m.u = 1.66 × 10-24 gm

(e) Size of nucleusRadius of nucleus is used to measure the size of the nucleus. The unit used for measuringthe size of the nucleus is Fermi (F). 1 Fermi = mThe radius of a nucleus is,   

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 Where R is radius of nucleus, A mass number and R o is a constant. R o = 1.2 Fermi

(f) Volume of nucleusSince nucleus is considered to be spherical, its volume could be found by using the formulafor the volume of the sphere.

Therefore, volume of the nucleus = V =

 

 V=  

 

 V=

 

 V    Volume of nucleus is directly proportional to its mass number (A).

(g) Density of nucleus As we know, density = mass/volumeMass of nucleus = total no. of nucleons * mass of one nucleon

=A×1 a.m.u

 Volume of nucleus =

 

Density of nucleus = 

   

 Density of nucleus is a constant number; therefore we can say that it is independent of theelement.

Classification of atoms based on nucleons

1.  IsotopesIsotopes are the atoms of same element having same atomic number, but different atomicmasses due to difference in number of neutrons in their nucleus.

Example of Isotopes:a.  Hydrogen has three isotopes,

1H1 Hydrogen (Protium), 1H2 Deuterium and 1H3 Tritium. b.  Chlorine has two isotopes, i.e., 17Cl35 and 17Cl37.c.  Oxygen has three isotopes, i.e., 8O16, 8O17 and 8O18 d.  Uranium has two isotopes, i.e., 92U235 and 92U238.e.  Carbon has 3 isotopes, i.e., 6C12, 6C13 and 6C14 

Here, it must be pointed out that practically every element has its isotopes. There areabout one thousand unstable isotopes of radioactive elements and 300 isotopes of stableelements. Isotopes differs in their mass number, therefore, isotopes differ in physicalproperties.

2.  Isobars Atoms of different elements, having same mass number, but different number of protons(atomic number) are called isobars. Isobars differ in number of electrons, protons andneutrons.

 An isobars differs in atomic number as well as number of protons, they differ in physical as well as in chemical properties.

Examples of Isobarsa.  18 Ar40 and 20Ca40 are isobars

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 b.  12Mg24 and 11Na24 are isobars.

3.  Isotones Atoms of different elements with same number of neutrons are called isotones. They differin number of electrons and protons.

Examples of isotones

14Si30 and 15P31 

Forces inside the nucleus

There are two major forces present inside the nucleusi.  Electrostatic force: this is repulsive force between the protons. This force depends on

the charge on the nucleons. Electrostatic force impact is felt at larger distance.ii.  Nuclear force: this is an attractive force among the nucleons. The impact of nuclear

force is felt only at very small distances within the nucleus. Hence nuclear force is calledshort range force. Nuclear force is independent of charge of nucleons.

 As the nuclear force is stronger than electrostatic force the nucleons do not fly apart.

Mass defect & Binding energy 

The difference between the expected mass and experimentally measured mass of nucleus iscalled mass defect. It is denoted by Δm. It can be calculated as follows:  Mass defect (Δm) = (expected mass of nucleus) - (measured mass of nucleus)

Δm = (sum of masses of protons and neutrons) - (measured mass of nucleus)

 When the nucleons are grouped together to form a nucleus, they lose a small amount of mass,i.e., there is mass defect. This mass defect is released as radiant energy according to therelation E = mc2;Thus

Energy released = mass defect × c2.This energy is used to bind nucleons together in the nucleus; therefore it is called bindingenergy.The smallest unit of binding energy for one a.m.u is generally mentioned in terms of MeV.

 Thus energy equivalent of 1 a.m.u of mass is 931.5 MeV.

If mass effect (Δm) is expressed in terms of a.m.u, then binding energy = Δm931.5 MeV 

In nuclear reactions, the energy that must be radiated or otherwise removed as binding energy may be in the form of electromagnetic waves, such as gamma radiation, or as heat.

 Average Binding energy 

 Average binding energy is the energy required to remove one nucleon from the nucleus.Binding energy per nucleon = Binding energy of the nucleus/ total number of nucleons

The stability of nucleus is understood in terms of binding energy per nucleons. More is the

 binding energy per nucleon, more is the stability.

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Graph of Binding energy per nucleon and mass number A 

The main observations from the graph are:a.  The binding energy per nucleon is smaller for lighter nuclei and increases with mass

number b.  The nuclei in the mass number range 40 to 120 are most stable as the binding energy 

per nucleon is more in their case. The peak value appears around A =60. The maximum binding energy per nucleon is for iron with a value of 8.7 MeV/nucleon.

c.  For nuclei with mass number higher than 120, the binding energy per nucleon starts

decreasing. The nuclei below 7.6 MeV/ nucleon like 92U238

are unstable.

Stability of Nuclei

There are several factors affecting nuclear stability, many of which are reflected in the abundance curve:

a.  As number of nucleon increases, attraction between nucleons increases also value of binding

energy increase, therefore stability of nuclei increases.

b.  Magic numbers: Nuclei which have 2,8,20,28,50,82 and 126 number of neutrons or protons are

more abundant in nature than other nuclei. This suggests that these nuclei are more stable than

others. The above sequence of numbers is called Magic numbers.

c.  Surface tension (unrequited bonds): smaller nuclei are less stable because they have Highsurface/volume ratios.

d.  Coulomb or electrostatic repulsion works against larger nuclei, because you pay a price stuffing

charge into a small volume. Although you always gain by adding more nucleons, but at large

distance nuclear force become weaker in comparison to electrostatic force

Just as every phenomenon tries to achieve stability, unstable nuclei try to achieve stability by throwing

out excess particles in the form of radiations. This gave rise to a phenomenon which was first observed

by Henry Becquerel. This phenomenon was called radioactivity by Madam Curie. 

Radioactivity 

The spontaneous disintegration of the nuclei with the emission of certain particles andradiations is called radioactivity. It is the phenomenon due to which certain elements given out

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highly penetrating radiations spontaneously. The activity of a radioactive substance is definedas the number of atoms disintegrating in one second. It is measured in various units. The SIunit of radioactivity is Becquerel.

a.  1 Becquerel (1 Bq) = 1 disintegration per second. b.  1 Curie (1 Ci) = disintegration per second = activity of 1 gm of pure radium

Causes of Radioactivity  As the atomic number and mass number increases, the size of the nucleus also increases.The increase in size leads to weakening of nuclear force and the repulsive force startsplaying a prominent role. In the element with atomic number Z=83 (Bismuth) the repulsiveforce just exceeds the attractive nuclear force, making the nucleus unstable. Emission startsoccurring from such unstable nucleus and then tries to attain stability by emitting particlesfrom inside it. This process of emission is known as radioactivity.

Radioactive elementsThe elements which give out high energy radiations on their own are called radioactive

elements.

Examples of Radioactive elements :1. Uranium 2. Thorium 3. Radium 4. Polonium.

Becquerel RaysThe original name for the radiations give out by radioactive elements is Becquerel rays.Properties of Becquerel rays:

a.  They affect photographic plate. b.  They ionize the gas through which they pass.c.  They can penetrate through matter. The range of penetration depends upon nature

of radioactive source and density of matter.d.  They are affected by electrostatic and magnetic fields.

Radioactive emission has three types of radiations – α, β and γ radiations 

Comparative Table of α, β and γ Radiations

Properties  -particles(2He4)   -particles(-1e0)   -rays

Name Are doubly chargedhelium nuclei

Electrons moving withhigh velocity 

Electromagnetic waves

Rest mass 6.64 10-27 kg 9.106 10-31 kg Nil  Velocity 1.4 to 2.3 107 m/s 1.1 to 2.96 108 m/s 3 108 m/sNature of charge Positive Negative Neutral

  Amount of charge + 3.2 10-19 C -1.6 10-19 C Nil

Specific chargeq

m

  4.8 107 C/kg 1.78 1011 C/kg Nil

  Wavelength Nil Nil 10-12 m to 10-14 mEffect of magneticfield

Slightly deflected Deflected more than  and opposite indirection to    

Not deflected

Effect of electrostatic field

Deflected towardsnegative plate

Deflected towardspositive plate

Not deflected

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Penetrating power 2.7 cm to 8.6 cm inair

5 mm of Al or 1 mm of lead

30 cm of iron

Relative ionizingpower

10,000 100 1

Laws of Radioactive Emission

1.  Rutherford and Soddy‟s law of Alpha Emission

  When a radioactive nuclide ejects an alpha particle, its mass number decrease by 4 andatomic number decreases by 2 such that the position of daughter nuclide is two places

 behind in the periodic table as compared to the parent nuclide.

Consider radioactive nuclide X with mass number A and atomic number Z, such that itejects an alpha particle. According to above law, the mass number of daughter nuclide will

 be A – 4 and atomic number Z – 2. Representing symbolically,

ZX A    Z- 2X A 4 + 2He4 Examples of  -decay 

92U238   90Th234 + 2He4 :

88Ra226   86Rn222 + 2He4

86Rn222   84Po218 + 2He4 :

84Po218   82Pb214 + 2He4 

2.  Rutherford and Soddy‟s law of Beta Emission 

 When a radioactive nuclide ejects beta particle, its mass number remains unaffected, butatomic number increases by one such that position of daughter nuclide is, one place aheadin the periodic table, as compared to the parent nuclei.

Beta emission generally takes place in such nuclides, which have far excess neutrons ascompared to protons. However, it is not a hard and fast rule. During beta emission, one of the neutrons breaks into an electron and proton, with release of energy. The proton remains

 within the nucleus, but the electron is ejected out.

Since number of nucleons in the parent nuclide remains same as in daughter nuclide,therefore, mass number remains unchanged. However, as one proton becomes more thanparent nuclide, therefore atomic number increases by one.

0n1    1p1 + -1e0 neutron proton electron

If X is the parent nuclide of mass number A and atomic number Z, such that it ejects betaparticle, then the mass number of daughter nuclide will be A, but atomic number will

 become Z+1. Representing symbolically,

ZX A    Z + 1X1 A + -1e0 

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Example of Beta Emission

11Na24   12Mg24 + -1e0 ;

6C14

 

 7N14

+ -1e0

;

15P32   16S32 + -1e0 

82Pb214   83Bi214 + -1e0 ;

83Bi214   84Po214 + -1e0 

3.  Gamma Emission

It has been found that the emission of alpha or beta particles is followed by the emission of 

gamma rays. This emission takes place, because either the parent nuclide or the daughternuclide is in excited state, i.e., they have excess energy than required to hold nucleonstogether.The gamma radiation takes away neither any mass nor charge from parent nuclide, andhence the mass number and atomic number remain unchanged.

Difference between Radioactive change and Chemical change

Radioactive change Chemical change1.  In radioactive change, the nucleus of 

an element on disintegration

produces completely new elementsand it is essentially a nuclearphenomenon.

2.  Radioactive change releases largeamount of energy.

3.  Radioactive disintegration is aspontaneous event.

4.  In radioactive disintegration, chargedparticles like alpha, beta are ejected.

1.  Chemical change does not producenew elements and it is not related to

the nucleus of the atom.2.  In a chemical change a very small

quantity of energy is released orabsorbed.

3.  Chemical change is an induced event.4.  In chemical change, no such ejection

of particles takes place.

Nuclear Fission

Nuclear fission is a nuclear reaction in which the nucleus of an atom splits into smaller parts(lighter nuclei), often producing free neutrons and photons (in the form of gamma rays), andreleasing a tremendous amount of energy. The two nuclei produced are most often of comparable but slightly different sizes, typically with a mass ratio of products of about 3 to 2,for common fissile isotopes. Nuclear fission was discovered by Ottohann and  Strassmann in1939.

Fission is usually an energetic nuclear reaction induced by a neutron. Fission of heavy elementsis an exothermic reaction which can release large amounts of energy both as electromagnetic

radiation and as kinetic energy of the fragments (heating the bulk material where fission takesplace). In order for fission to produce energy, the total binding energy of the resulting elements

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must be greater than that of the starting element. Fission is a form of nuclear transmutation because the resulting fragments are not the same element as the original atom.

Nuclear fission produces energy for nuclear powerand to drive the explosion of nuclear weapons. Both

uses are possible because certain substances callednuclear fuels undergo fission when struck by fissionneutrons, and in turn emit neutrons when they 

  break apart. This makes possible a self-sustainingchain reaction that releases energy at a controlledrate in a nuclear reactor or at a very rapiduncontrolled rate in a nuclear weapon.

Most general nuclear fission reaction is given below:

92U235

+ 0n1

  56Ba141

+ 36Kr92

+3 0n1

+ Q Where Q is the energy released in nuclear fission.

In the above reaction 1 neutron produces 3 neutrons, which collide with another 3 nuclei of uranium, which produces another 9 neutrons. So this reaction rapidly increases till all uraniumused. This is example of an uncontrolled chain reaction.

For controlled chain reaction, following precautions has to be taking in nuclear plants.

a.  The nuclear reactors should be embedded in thick concrete walls so as to prevent any leakage of gamma radiations or neutrons.

 b.  The nuclear material must be kept in thick lead containers, with narrow mouth and plugged with thick lead corks.

c.   Workers in nuclear establishments must wear lead lined aprons and gloves. They must wearspecial lead glasses to protect eyes.

d.   Any nuclear material should be handled with mechanical tongs.e.  The workers must wear special film badges. These badges can absorb nuclear radiation

 which can be tested to find the amount of radiation absorbed by a particular worker.f.   A periodic compulsory medical checkup should be done. If a particular person is found be

done. If a particular person is found over-exposed to the nuclear radiation, he should beimmediately withdrawn from the nuclear establishment.

Nuclear Fusion

Nuclear fusion is the process by which two or more atomic nuclei join together, or "fuse", toform a single heavier nucleus. This is usually accompanied by the release or absorption of largequantities of energy. Fusion is the process that powers active stars, the hydrogen bomb andexperimental devices examining fusion power for electrical generation.

The fusion of two nuclei with lower masses than iron (which, along with nickel, has the largest binding energy per nucleon) generally releases energy, while the fusion of nuclei heavier thaniron absorbs energy. This means that fusion generally occurs for lighter elements only, andlikewise, that fission normally occurs only for heavier elements

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Creating the required conditions for fusion on Earth is very difficult, to the point that it has not  been accomplished at any scale for Protium, the common light isotope of hydrogen thatundergoes natural fusion in stars. In nuclear weapons, some of the energy released by anatomic bomb (fission bomb) is used to compress and heat a fusion fuel containing heavierisotopes of hydrogen, and also sometimes lithium, to the point of "ignition". At this point, the

energy released in the fusion reactions is enough to briefly maintain the reaction.

Fusion-based nuclear power experiments attempt tocreate similar conditions using less dramatic means,although to date these experiments have failed tomaintain conditions needed for ignition long enoughfor fusion to be a viable commercial power source.

Fusion reaction which occurs in stars and sun is following:

1H2

+ 1H3

2He4

+ 0n1

+ Q

Where Q is the energy released in single fusion.

Formulae

a.  Mass of Neutron Mass of Proton

 b.  Number of Proton = Number of Electron = Atomic Number

c.  Number of Neutron = Mass Number – Atomic Number i.e., n = A – Z

d.  Charge on Electron = -1.6 10-19 Coulomb

e.  Charge on Proton = + 1.6 10-19 Coulomb

f.  Charge on Neutron = 0

g.  Mass of Electron = 9.1 10-31 kg

h.  Mass of Proton = 1.6 10-27 kg

i.  1 eV = 1.6 10-19 Joule

 j.  1 a.m.u = 931 MeV 

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Problems

1.   What do you mean by :

(a) Atomic number(b) Mass number of a nucleus?

2.   What are isobars ? Give one example.

3.   What is radioactivity? Name two radioactive substances.

4.  (i) What are ,   and   -radiations composed of?

(ii) Which has least penetrating power?

5.  How are   -radiations produced?

6.   An  -particle absorbs an electron. What does is change to?

7.   What type of change takes place in the nucleus when a   -particle is emitted?

8.   A nucleus of radioactive phosphorus has atomic number 15 and mass number 32.(i) If stable isotope of the above mentioned nucleus has one neutron less, what are the

atomic number and mass number of the isotope?(ii) If the radioactive isotope emits a   -particle. What are the atomic number and mass

number of the new nucleus?

9.  The element 11Na24 emits a   -particle to change into Mg. Write the symbolic equation for

the change. What are the numbers 11 and 24 called ? What do they signify for the elementNa ?

10.   An  -particle absorbs two electrons. What does it change to ?

11.   A nucleus of 88Ra226 emits an  -particle. Represent the charge by an equation. Identify thenew nucleus formed, from the following :

84Po, 85 At, 86Rn, 87Fr

12.   Why do isobars have different chemical properties ?

13.   A radioactive element zX A loses two successive   -particles and then an  -particle such that

the resulting nucleus is Q Y P. Find the values of P and Q.

14.   What do you understand by the term chain reaction?

15.   Why is it difficult to start a fusion reaction?

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Objective Problems

1. 

The mass of an electron is equal to(a) 9.1 10-31 kg (b) 9.1 10-30 kg(c) 9.1 10-27 kg (d) none of these

1.   What is the particle Y in the following nuclear reaction ?

4Be9 + 2He4   6C12 + Y (a) Electron (b) Neutron (c) Proton (d) None of these

2.  Nucleons correspond to the number of (a) Electrons (b) protons (c) neutrons (d) neutrons and protons

3.  The mass of an atom is expressed in(a) kg (b) g (c) a.m.u. (d) Carats

4.  The specific charge of an electron is equal to(a) – 1.76 1011 C kg-1 (b) 1.76 10-11 C kg-1 (c) 1.602 10-19 C (d) – 1.602 10-19 C

5.  In the following nuclear reaction, how many alpha particles are given out ?

92X234   88 Y 218 (a) 2 (b) 3 (c) 4 (d) 6

6.  The number of neutrons contained in 92U238 is(a) 92 (b) 146 (c) 238 (d) 330

7.  In the following nuclear reaction, what is the element X ?i.  7N14 + 2He4   1H2 + X

(a) 8O16 (b) 7N14 (c) 9F17 (d) 10Ne17 

8.  The number of electrons contained in the nucleus of 92U235 is(a) 92 (b) 143 (c) 235 (d) zero

9.   An element X with mass number A and atomic number Z is represented by (a) X (b)  A XZ (c) ZX A  (d) ZX A – Z

10.  The process of fusion is used for constructing a(a) atom bomb (b) ordinary bomb (c) hydrogen bomb (d) neutron bomb

11.  In a nuclear reactor, the moderator is(a) uranium – 234 (b) uranium – 238 (c) cadmium (d) heavy water

12.  Radioactivity was discovered by (a) Rutherford (b) Becquerel (c) Bohr (d) Madame Curie

13.  The discovery of neutron was made by 

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(a) Chadwick (b) Rutherford (c) Becquerel (d) Curie

14.   Which of the following has the least penetrating power ?(a) Alpha particles (b) Beta particles(c) Gamma rays (d) All have the same penetrating power

15.  The fuel used in nuclear reactors is(a) U – 235 (b) U – 236 (c) U – 234 (d) U – 238

16.  The longest and shortest wavelengths (in microns) for red and violet colours arerespectively given by (a) 0.4, 0.7 (b) 0.3, 0.6 (c) 0.7, 0.9 (d) none of these

17.  The fission of uranium – 235 by means of slow moving neutrons is called a/an(a) chain reaction (b) irreversible chemical reaction(c) explosion (d) none of these

18.   Which amongst the following can cause the fission of U – 235 to yield a chain reaction ?(a) Slow electrons (b) Slow protons (c) Slow neutrons (d) Fast neutrons

19.  The release of energy when fission occurs in a nuclear chain reaction is the basis of (a) atom bomb (b) hydrogen bomb (c) neutron bomb (d) none of these

20.   A hydrogen bomb is a(a) controlled nuclear fission (b) uncontrolled nuclear fission(c) uncontrolled nuclear fusion (d) controlled nuclear fusion

21.   Which of the following will produce lesser pollution problems ?(a) Nuclear fission(b) Nuclear fusion(c) Both will produce the same amount of pollution(d) Nothing can be decided

22.   Which of the following radiations is most dangerous because of its high penetrating powerand high energy?(a) Alpha particles (b) Beta particles (c) Gamma rays (d) None of these

23.  The nucleus resulting from 238U92 after successive loss of tw0 alpha and four beta particles

isa)238 TH 90  b) 230 Pu 94 c) 230 Ra 88 d) 230 U 92

24.   An isotone of 76Ge32 isa) 77 Ge 32 b) 77 As 33 c) 77Se 34 d) 77Se 36

25.  If Uranium (mass number 238 and atomic number 92) emits an α particle, the product hasmass number and atomic numbera) 236and 92 b) 234and90 c) 238and90 d) 236and90 

26.   Which of the following in an isotope of 32 Ge 76 ?

a) 33 As 77 b) 32 Ge 77 c) 34 Se 77 d) 35 Br 80 

27.  The atomic number of a radioactive element increases by one unit in :

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a) alpha emission d) beta emission c) gamma emission d) electron capture

28.  Sulphur -35 (34.96903 a. m. u) emits a particle but no ray. The product is chlorine35(34.96885 a.m.u.). The maximum energy of the particle emitted isa) 0.00018 MeV b) 930MeV c) 0.16758 MeV d) 1.6758 MeV 

29.   Which of the following is a magic number?a) 54 b) 10 c) 20 d) 18

 ANSWER KEY 

CHAPTER # 3

PROBLEMS

1. I = 250 mA = 250 10-3 A, t = 8 sec We know that,

I =Q

t  

Q = I tQ = 250 10-3  8Q = 2000 10-3 = 2 C

2. (a) Let resistance between P and Q is R PQ.3 and 3 are in series. So,

R S = 3 + 3 = 6  R S and 3 are in parallel. So,

R PQ = 33

S

S

 R R

 

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=3 6

3 6

 

R PQ =18

9= 2  

(b) Let resistance between A and B is R  AB. 

3 , R PQ and 3 resistors are in series. So,R  AB = 3 + R PQ + 3R  AB = 3 + 2 + 3 = 8  

3. Resistance of 1 and 2 are in series. So,R S = 1 + 2 = 3  

R S and 1.5 are in parallel. So,

R eq =1.5

1.5

S

S

 R

 R

 

R eq =3 1.5 4.5

3 1.5 4.5

= 1  

4. When resistors are in parallel, then

R P =2 2

2 2r 

 

R P =4

4+ r = 1 + r

Let r = Internal resistance.Current IP = 1.2 A 

  = IP (R P + r)

= 1.2 (1 + r)= 1.2 + 1.2 r … (i) 

 

2

2

r

 

 Again, when resistances are in series, thenR S = 2 + 2 = 4R eq = 4 + rIS = 0.4 A 

r

2 2

 + -

 Thus,

  = IS (R S + r)

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= 0.4 (4 + r)= 1.6 + 0.4 r … (ii) 

From equations (i) and (ii) we have,  - 1.2 r = 1.2 … (i)   - 0.4 r = 1.6 … (ii) 

  - 1.2 r = 1.2 … (i) 3  1.2 r = -4.8 … (iii) 

-2   = -3.6

  =3.6

1.82

volt

 Again form equation (i) we get,  - 1.2 r = 1.2

1.2 r =   - 1.2

or, r =1.8 1.2

1.2

 

= 0.6 0.51.2  

5. Equivalent resistance = 2 + 0.7 + 4.5 = 7.2    = 1.8 V 

Current in the circuit (I) =1.8

7.2= 0.25 A 

(a) Reading of ammeter = 0.25 A (b) Let terminal potential of the battery be V then,

  = I (R + r)  = IR + Ir

i.e.,   = V + Iror, V =   - Ir

 V = 1.8 – 0.25 2 = 1.3 volt

6. R =1

( / 4 )a   and R 1 =

31

( / 2 )a    

1 (31) /( / 2)

1/( / 4)

 R a

 R a

  

    

=3 2 3

4 2

 

R 1 : R = 3 : 2

7. We know that,

1 1

2 2

1

1

 R

 R  

2 12

1

11

R

 R

 

=16.25 75

3.25

 

= 375 cm

8. Net e.m.f. = 1.5 volt

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Total internal resistance,1 1 1 1 3

2 2 2 2 pr   

2

3 p

r   

Total resistance =7 2 9

33 3 3

 

Current through the resistor =1.5

0.53

V  A

 R  

9. We have,P = 60 W, V = 250 V 

P = VI

I =P

V  

=60

250= 0.24 Amp

10. We have, V = 4 V, I = 0.5 A, r = 2.5  (i) Energy = V  I t

E = 4 0.5 600 ( t = 10 60 = 600 sec)= 1200 Joule

(ii) As e.m.f. of battery = 4 V then,

e.m.f. = IC (R + r)

R =e.m.f 

I- r

=4

2.50.5

 

R = 8 – 2.5 = 5.5  

(iii) P = V R I= 2.75 0.5 ( V  R = 5.5 0.5 = 2.75 V)= 1.375 W 

Energy dissipated = 1.375

10

60= 825 Joule

11. We have,P1= 60 W, V 1 = 220 V, P2 = 60 W, V 2 = 110 V 

2

1

1

1

V  R

P  

=220 220

60

 

and, 2

110 110

60

 R

 

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1

2

220 220

60110 110

60

 R

 R

 

=

220 220 4

110 110 1

 So, R 1 : R 2 = 4 : 1

12. We have,P1 = 100 W, P2 = 200 W 

1 2

2 1

1, when V isconstant

 R P R

  R P P

 

  1

2

200

100

 R

 R  

So, R 1 : R 2 = 2 : 1

13. We have,R 1 = 4 , R 2 = 6 , V = 6 Volt

Req =4 6

4 6

= 2.4 (As R 1 and R 2 in parallel)

(i)2V

P =Req

 

=6 6

2.4

 

=36

2.4= 15 W 

(ii) Since, potential across each resistor is same , so,2

1

1

V P

 R  

=6 6

94

and,

2

2

2

P  R  

=6 6

6

= 6 W 

P1 = 9 W, P2 = 6 W 

14. We have,P1 = 50 W, V = 220 V P2 = 100 W, V = 220 V If both are connected in series then their resistances add upto form an equivalentresistance. And current is same in series arrangement.

2

1

1

V  R

P  

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=220 220

96850

 

2

2

2

V  R

P  

220 220 484100

 

Req = 968 + 484 = 1452  220

0.151452

 I  A 

Now potential drop across R 1  V 1 = I R 1 = 0.15 968 = 145.2 V 

 And potential drop across R 2  V 2 = I R 2 = 0.15 484 = 72.6 V 

Power dissipated in R 1 = V 1I= 145.2 0.15 = 21.78 W 

Power dissipated in R 2 = V 2I= 72.6 0.15 = 10.89 W 

Power dissipated in first lamp is more in comparison the second because resistanceof first lamp R 1 is greater than the resistance R 2 of the second lamp.

15. 2V 

P R

 

2V 

 R P

 

=220 220

484100

 

 V = IR V 

 I  R

 

=220

484 

= 0.45 A 

16. (i)1

V  R  

=150

12 

= 75  

(ii) Energy produced in 1 minute P = IV  1 60= 0.2 15 60= 180 Joule

17. Energy produced in 5 minutes P = IV  5 60= 0.5 6 5 60= 900 Joule

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18. 2

1t 

V  (R and P is constant)

2

1 2

2

2 1

t V 

t V   

2

5 200 200

220 220t 

 

2

5 220 220

200 200t 

 

= 6.05 minutes

19. P

 I V 

 

=24

12

2 A 

Energy liberated in 20 minutes (20 60 sec)= 24 20 60= 28,800 Joule

20. kWh =1000

VIt V  V IR I  

 R

 

=2

1000

V t 

 R  

=

200 200 5

200 1000 60

 

= 0.0167 kWh

OBJECTIVE PROBLEMS

1. D 2. B 3. A 4. D 5. B 6. A 7. A

8. C 9. B 10. C 11. D 12. D 13. D 14. B

15. A 16. B 17. D 18. A 19. D 20. A 21. B

22. C 23. A 24. C 25. A 26. A 27. C

CHAPTER # 4

PROBLEMS

1. No. Because at any point on this line, tangent gives the direction of magnetic field. But atthe intersection point, we obtain two tangents, i.e. two directions of magnetic field, which is not

possible.

2. Yes. The face of circular coil for which the direction of current is anticlockwise behaves asNorth pole while the face having clockwise direction of current behaves as South pole.

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3. (i) By increasing the strength of current.(ii) By increasing the number of turns per unit length.(iii) By introducing a soft iron core in the solenoid.

4. When a coil is rotated in a strong magnetic field then the magnetic flux linked with coilchanges with time. This change in flux results in an induced current in the coil. Thedirection of induced current is giv en by Fleming‟s Right Hand rule. 

5. When a current carrying coil is placed in a strong magnetic field then it experiences atorque on it. The direction of this torque is given by Fleming‟s Left Hand rule. 

6. The speed of an electric motor depends on(i) the number of turns in the coil(ii) the strength of current(iii) the strength of the magnetic field.

7. In 1831, Michael Faraday introduced electromagnetic induction. According to him, if themagnetic flux linked with a closed circuit changes then an induced e.m.f. (induced current)is set up in that circuit. This phenomenon is called as electromagnetic induction.

8.  “The induced current in a coil will appear in such a direction that it opposes the change inmagnetic flux which is responsible for its production”. 

9. D.C. Motor A.C. generator(i) A D.C. motor changes electrical energy 

into mechanical energy.

(ii) It works on the principle that when anelectric current is passed through aconductor placed in a magneticfield, the conductor starts moving as aresult of force acting on it.

 A simple A.C. generator changes mechanical

energy into electrical energy.

It works on the principle that whenmagnetic flux passing through a closedcircuit changes, it results in the induction of an e.m.f. thereby current flows in the coil.

10. Transformers are used in electric circuit and devices which operate at a voltage other thanthe supplied voltage.No, they cannot be used with a direct current source.

11. As, NP = 800, NS = 8, EP = 220 V, ES = ?

S S

P P

N E

N E  

SS P

P

NE E

N  

=8

220800

 

= 2.2 Volt.

OBJECTIVE PROBLEMS

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1. B 2. D 3. B 4. A  5. B 6. C

7. B 8. D 9. C 10. C 11. A  12. B

13. B 14. A  15. D 16. D 17. B 18. A 

19. C 20. A 

CHAPTER # 5

PROBLEMS

1.  (a) The total number of protons presents in the nucleus of an atom is known as the atomicnumber of that element.

(b) The total number of protons and neutrons present in the nucleus of an atom is known asthe mass number of that element.

2.  The atoms of different elements which have the same mass number but different atomicnumbers, are called isobars. Eg. 11Na23 and 12Mg23.

3.  Radioactivity is that nuclear phenomenon in which spontaneous emission of radiationoccurs. Such substances are called radioactive substances, e.g., Uranium, Radium,Thorium, and Polonium, etc.

4.  (i)   -particles are composed of helium nucleus (2He4).

   -particles are composed of electrons (-1e0).

  -radiations are electromagnetic radiations composed of    -rays photons.

(ii)  -particles have least penetrating power.

5.   After   or   -emission, the nucleus acquires the excited state, i.e., it has excess of energy.

This excess of energy is emitted in the form of    -rays photon.

6.  It changes to ionised helium atom i.e. now it carries only one unit positive charge.

7.   A neutron of nucleus is converted to an electron and a Proton, when a   -particle is emitted.

1.  0n1    +1P1 + -1e0 + v ii.  Neutron Proton Electron Antinutrino 

8.  (i) Atomic number = 15i.  Mass number = 31

(ii) Atomic number = 16

ii.  Mass number = 32

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9.  11Na24   12Mg24 + -1   0 

The numbers 11 and 24 are called the atomic number and mass number respectively. They tell the number respectively. They tell the number of protons and neutrons in that element.

10. It changes to the neutral atom of helium.

11. The new nucleus formed is 86Rn

88Ra226   86Rn222 + 2He4 (  -particle) 

12. Isobars have different atomic numbers, i.e., different number of protons, hence they havedifferent chemical properties.

13. P = A – 4 and Q = Z.

14. On the fission of one heavy nucleus more neutrons are produced which further disintegrateother nuclei resulting in a chain of fission is formed. Such reaction is called chain reaction.

15.  because to start a fusion reaction, high temperature and pressure is required.

Objective Problems

1. A  2. B 3. D 4. C 5. A  6. C 7. B

8. A  9. D 10. C 11. C 12. D 13. B 14. A 

15. A  16. D 17. A  18. A  19. C 20. A  21. C

22. B 23. C


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