2 Marks Questions

Question 12 Marks

What is mass defect? Explain binding energy of the nucleus and the binding energy per nucleon.
Explain binding energy of nucleus.

Answer

$\rightarrow$ The nucleus is made up of neutrons and protons.
Therefore, it may be expected that the mass of the nucleus is equal to the total mass of its individual protons and neutrons.
$\rightarrow$ But the nuclear mass $M$ is found to be always less than the total mass of its individual protons and neutrons.
$\rightarrow$ For example :
${ }_8 O ^{16}$, a nucleus which has $8$ neutrons and $8$ protons.
Mass of $8$ neutrons $=8 \times 1.00866 u$
Mass of $8$ protons $=8 \times 1.00727 u$
Mass of $8$ electrons $=8 \times 0.00055 u$
$\rightarrow$ Therefore, the expected mass of ${ }_8 O ^{16}$ nucleus
$=(8 \times 1.00866+8 \times 1.00727)$
$=8(1.00866+1.00727)$
$=8 \times 2.01593 u$
$=16.12744 u$
$\rightarrow$ The atomic mass of ${ }_8 O ^{16}$ found from mass spectroscopy experiments is seen to be $15.99493 u$
$\rightarrow$ Subtracting the mass of $8$ electrons $(8 \times 0.00055 u=0.0044 u)$ from this we get the experimental mass of ${ }_8 O ^{16}$ nucleus to be $15.99053 u$.
$\rightarrow$ Thus, the mass of the ${ }_8 O ^{16}$ nucleus is less than the total mass of its constituents by
$(16.12744-15.99053)=0.13691 u \text {. }$
$\rightarrow$ "The difference in mass of a nucleus and its constituents, $\Delta M$ is called the mass defect" and is given by
$\Delta M =\left[ Z m_p+( A - Z ) m_n\right]- M$
Where$, Z =$ number of protons
$A - Z = N =$ neutron number
$m_p-$ mass of proton
$m_n-$ mass of neutron
$M -$mass of a nucleus
$\rightarrow$ The energy equivalent to this mass defect is called the binding energy of nucleus.
$\therefore$ Binding energy $E _b=\Delta M c^2$

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Question 22 Marks

Explain controlled thermonuclear fusion.

Answer

→The natural thermonuclear fusion process in a star is a replicated in a thermonuclear fusion device.
→In controlled fusion reactors, the aim is to generate steady power by heating the nuclear fuel to a temperature in the range of $10^8 K$. At these temperature the fuel is a mixture of positive ions and electrons (plasma).
→The challenge is to confine this plasma, since no container can stand such a high temperature. →Several countries around the world including India are developing techniques in this connection. If successful, fusion reactors will hopefully supply almost unlimited power to humanity.

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Question 32 Marks

Give the information about charge and atomic number of the nucleus.

Answer

→The positive charge in the nucleus is that of the protons. A proton carries one unit of fundament charge $\left(e=1.6 \times 10^{-19} C \right)$ and is stable.
→ All the electrons of an atoms are outside the nucleus. The number of electrons outside the nucleus are same as atomic number Z .
→Hence total charge of electron of atom is - Ze (negative charge). Since the atom is neutral, the charge of the nucleus is + Ze .
→Hence, the number of protons in the nucleus of the atom is the atomic number Z .

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Question 42 Marks

Explain the process of thermonuclear fusion as a source of energy in the Sun.

Answer

$\rightarrow$ Sun continuously emits energy due to thermonuclear fusion.
The interior of the Sun has a temperature of $1.5 \times 10^7 K$.
$\rightarrow$ The thermonuclear fusion process in the Sun is known as proton $-$ proton cycle.
$\rightarrow$ This process is a multi $-$ step process in which the hydrogen is burned into helium.
Thus the fuel in the Sun is the hydrogen in its core.
$\rightarrow$ The proton $-$ proton cycle is represented by the following sets of reactions :
${ }_1^1 H +{ }_1^1 H \rightarrow{ }_1^2 H +e^{+}+v+0.42 MeV$
$........(i) e^{+}+e^{-} \rightarrow \gamma+\gamma+1.02 MeV$
$........(ii) { }_1^2 H +{ }_1^1 H \rightarrow{ }_2^3 He +\gamma+5.49 MeV$
$ ......(iii) { }_2^3 He +{ }_2^3 He \rightarrow{ }_2^4 He +{ }_1^1 H +{ }_1^1 H +12.86$
$MeV........(iv)$
$\rightarrow$ In this reaction, the first three reactions must occur twice and in the fourth reaction two light helium nuclei unite to form ordinary helium nucleus.
$\rightarrow$ If we consider the combination
$2 \text { (i) }+2 \text { (ii) }+2 \text { (iii) }+ \text {(iv)}, $ the net effect is
$4_1 H ^1+2 e^{-} \rightarrow{ }_2 He^4+2 v+6 \gamma+26.7 MeV$
$\text { OR }$
$4_1 H ^1+4 e^{-} \rightarrow\left[{ }_2 He ^4+2 e\right]+2 v+6 \gamma+26.7 MeV$
$\rightarrow$ Thus four hydrogen atoms combine to form an ${ }_2 He ^4$ atom with a release of $26.7 MeV$ of energy.

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Question 52 Marks

Draw the nature of the graph of binding energy per nucleon against atomic mass number and explain its notable points.

Answer

→Figure is a plot of the binding energy per nucleon $E _{b n}$ versus the mass number A . The main features of the plot are as given below :
(i) the binding energy per nucleon $E _{b n}$ is practically constant, i.e. practically independent of the atomic number for nuclei of middle mass number $(30< A <170)$. The curve has a maximum of about 8.75 MeV for $A =56$ and has a value of 7.6 MeV for $A =238$.
(ii) $E _{b n}$ is lower for both light nuclei $( A <30)$ and heavy nuclei $( A >170)$.

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Question 62 Marks

Explain the relationship between mass and energy from Einstein's theory of special relativity.

Answer

→Einstein's Special Theory of Relativity showed that mass and energy are equivalent to each other
→Before the advent of this special theory of relativity it was presumed that mass and energy were conserved separately in a reaction.
→However Einstein showed that mass is converted to energy and energy to mass. It means mass is another form of energy.
→Mass is converted into kinetic energy or other forms of energy.
→mass-energy equivalence relation
$E =m c^2$
Where, $m=$ decaying mass
$c=$ velocity of light in vacuum
$c=3 \times 10^8 ms^{-1}$
→Experimental verification of the Einstein's massenergy relation has been achieved in the study of nuclear reactions amongst nucleons, nuclei, electrons and other more recently discovered particles.
→In a reaction the conservation law of energy states that the initial energy and the final energy are equal provided the energy associated with mass is also included.

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Question 72 Marks

Write a short note : Size of the nucleus
###
How the radius of the nucleus is estimated?
Explain.

Answer

→Rutherford was the pioneer to visualize the nucleus of an atom. For this he studied the emission of $\alpha$-particle by thin gold foil.
→The experiment revealed that the distance of closest approach to a gold nucleus of an $\alpha$-particle of kinetic energy 5.5 MeV is about $4.0 \times 10^{-14} m$.
→From this, Rutherford suggested that the actual size of the nucleus has to be less than $4.0 \times 10^{-14} m$.
→If we use $\alpha$-particles of higher energies than 5.5 MeV , the distance of closest approach to the gold nucleus will be smaller.
→Using fast electrons as projectiles instead of $\alpha$-particles, the sizes of the nuclei of various elements can be accurately measured in scattering experiments.
→The relation between radius of nucleus and mass number A
$R=R_0 A^{\frac{1}{3}}$
Where, $R _0=1.2 \times 10^{-15} m$
$\left(=1.2 fm ; 1 fm =10^{-15} m\right)$
→This means the volume of the nucleus which is proportional to $R ^3$ is proportional to A . Thus density of nucleus is constant, independent of A, for all nuclei.
→Different nuclei are like a drops of liquid of constant density.
→The density of nuclear matter is approximately $2.3 \times 10^{17} kg m ^{-3}$. This density is very large compared to water which is $10^3 kg / m ^3$.
→Since the density of nucleus is very large, the entire mass is concentrated in the nucleus. As a result, the atom is largely hollow.

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Question 82 Marks

Briefly explain the discovery of neutrons.

Answer

→Neutron was discovered by a scientist named Chadwick.
→Chadwick observed emission of neutral radiation when beryllium nuclei were bombarded with $\alpha$-particle. ( $\alpha$-particle is made up of a helium nucleus)
→In addition he observed that this neutral radiation could knock out protons from light nuclei such as those of helium, carbon and nitrogen.
→The only neutral radiation known at that time was photons. (electromagnetic radiation)
→Application of the principles of conservation of energy and momentum showed that if the neutral radiation consisted of photons, the energy of photons would have to be much higher than is available from the bombardment of beryllium nuclei with $\alpha$-particles.
→From conservation of energy and momentum, the mass of new particle (neutron) was found to be as very nearly the same as mass of proton.
→ Currently, the mass of neutron
$m_n=1.00866 u=1.6749 \times 10^{-27} kg$
→Chadwick was awarded the 1935 Nobel prize in physics.
→A free neutron, unlike a free proton is unstable.

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Question 92 Marks

Write short note on Nuclear Force.

Answer

→Nucleus contains protons and neutrons, in which there is a coulomb repulsion between protons and protons. However, the proton can not escape from the nucleus. Because to bind a nucleus together there must be a strong attractive force of a totally different kind. It must be strong enough to overcome the repulsion between (the positively charged) protons and to bind both protons and neutrons into the tiny nuclear volume.
→Many features of the nuclear binding force are summarised below :
(i) The nuclear force is much stronger than the Coulomb force acting between charges or the gravitational forces between masses. That's why it holds protons and neutrons in the nucleus.
(ii) The range of the nuclear force is of the order of femtometres. For distances greater than one femtometres this force rapidly decreases to zero.
→This leads to saturation of forces in a medium or a large sized nucleus.
→A plot of the potential energy between two nucleons as a function of distance as shown in figure.

→The potential energy is minimum at a distance $r_0$ of about 0.8 fm .The force is attractive for distance larger than 0.8 fm .
→The force is repulsive for distance less than 0.8 fm .
(iii) The nuclear force between neutronneutron, proton-neutron and proton-proton is approximately the same. The nuclear force does not depend on the electric charge.
→Unlike Coulomb's law or the Newton's law of gravitation there is no simple mathematical form of the nuclear force.

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Question 102 Marks

Explain the unit of mass.

Answer

→The mass of an atom is very small compared to a kilogram. Kilogram is not a very convenient unit to measure such small quantities.
→'Atomic mass unit' is used to measure the mass of an atom.
• Definition :
→The twelfth part of the mass of unexcited carbon $\left( C ^{12}\right)$ atom is called $1 u$ (amu).
$1 u=1.66 \times 10^{-27} kg$
(approximate mass of proton)
→"A technique called mass spectrography is used to measure the mass of atom".
→Accurate measurements of atomic masses is carried out with a mass spectrometers.

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Question 112 Marks

Explain nuclear energy.

Answer

→The curve of binding energy per nucleon versus mass number A is shown in figure.
→The binding energy per nucleon is nearly constant ( 8 MeV ) in the region between $A =30$ to $A =170$.
→For the lighter nuclei region $A <30$ and for the heavier nuclei region $A >170$ the binding energy per nucleon is less than 8.0 MeV .
→If nuclei with less total binding energy transform to nuclei with greater binding energy there will be a net energy release.
→"When a heavy nucleus decays into two or more intermediate mass fragments, then the total binding energy increases. Energy is released during this process. This process is called nuclear fission".
→"When two or more light nucleus fuse into heavier nucleus then also the total binding energy increases. Due to this energy is realeased during this process. This process is called nuclear fusion".
→Exothermic chemical reactions underlie conventional energy sources such as coal or petroleum. Here the energies involved are in the range of electron volts. On the other hand, in a nuclear reaction, the energy release is of the order of MeV .
→ Thus for the same quantity of matter, nuclear sources produce a million $\left(10^6\right)$ times more energy than a chemical source.
→ For example :
→ Fission of 1 kg of uranium generates $10^{14} J$ of energy compare it with burning of 1 kg of coal that give $10^7 J$.

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Question 122 Marks

What is nucleus? Give a general introduction.

Answer

→The central part of an atom is called nucleus. The nucleus contains the positive charge of the atom and mass densely concentrated at the centre of the atom.
→The dimensions of a nucleus are much smaller than those of an atom.
→Rutherford's experiments on scattering of $\alpha$ particles demonstrated that the radius of a nucleus was smaller than the radius of an atom by a factor of about $10^4$.
→From this we can say that the volume of a nucleus is about $10^{-12}$ times the volume of the atom.
→In other words the atom is almost empty.
→If an atom is enlarged to the size of a classroom, the nucleus would be of the size of pinhead.
→ The nucleus contains most (more than $99.9 \%$ ) of the mass of an atom.

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Question 132 Marks

Give a brief explanation about Radioactivity.

Answer

→Becquerel discovered radioactivity in 1896 purely by accident.
→While studying the fluorescence and phosphorescence of compounds irradiated with visible light, Becquerel observed a phenomenon.
→After illuminating some pieces of uranium - potassium sulphate with visible light, he wrapped them in black paper and separated the package from a photographic plate by a piece of silver. When, after several hours of exposure, the photographic plate was developed.
→By doing this, blackness appeared on the photographic plate.
→This blackness must be due to some radiation emitted from the compound.
→Experiments performed subsequently showed that radio activity was a nuclear phenomenon in which an unstable nucleus undergoes a decay. This is referred to as radioactive decay.
→Three types of radioactive decay occur in nature.
(i) $\alpha$-decay in which a helium nucleus ${ }_2 He ^4$ ( $\alpha$-particles) is emitted.
(ii) $\beta$-decay in which electrons or positrons are emitted.
(Positron : particles with the same mass as electron, but with a charge exactly opposite to that of electron.)
(iii) $\gamma$-decay in which high energy (hundreds of $k e V$ or more) photons are emitted.

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Question 142 Marks

Explain the thermonuclear fusion from the fusion of helium atom in the interior of a star and the Red Giant of the Sun.

Answer

→Helium is not only element that can be synthesized in the interior of a star. As the hydrogen in the core gets depleted and becomes helium, the core starts to cool. The star begins to collapse under its own gravity which increases the temperature of the core. If this temperature increases to about $10^8 K$ fusion takes place again this time of helium nuclei into carbon. This kind of process can generate through fusion higher and higher mass number elements. But elements more massive than those near the peak of the binding energy curve in $E _{b n} \rightarrow$ A graph can not be so produced.
→The age of the Sun is about $5 \times 10^9 y$ and it is estimated that there is enough hydrogen in the sun to keep it going for another 5 billion years.
→After that, the hydrogen burning will stop and the sun will begin to cool and will start to collapse under gravity, which will raise the core temperature. The outer envelop of the sun will being to expand and the sun will become a 'Red Giant' will turn into position.

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