Nuclear Fission, Fusion and Nuclear Reactor Questions in English

(D) The power $P$ is given as $200\, MW = 200 \times 10^6\, W$.
Time $t$ in one day is $24\, \text{hours} = 24 \times 3600\, \text{seconds} = 86400\, \text{s}$.
Energy $E$ is calculated as $E = P \times t$.
$E = (200 \times 10^6\, \text{W}) \times (86400\, \text{s})$.
$E = 200 \times 10^6 \times 86400\, \text{J} = 17280000 \times 10^6\, \text{J}$.
$E = 1728 \times 10^{10}\, \text{J}$.
Therefore, the correct option is $D$.

(C) The binding energy of a nucleus is given by the product of the number of nucleons and the binding energy per nucleon.
For the reactant,two deuterons $(1^2H)$ are involved. Each deuteron has $2$ nucleons.
Total binding energy of two deuterons $= 2 \times (2 \times 1.112 \, MeV) = 4 \times 1.112 \, MeV = 4.448 \, MeV$.
For the product,one $\alpha$-particle $(2^4He)$ is formed. It has $4$ nucleons.
Total binding energy of one $\alpha$-particle $= 4 \times 7.047 \, MeV = 28.188 \, MeV$.
The energy released $Q$ in the fusion reaction is the difference between the total binding energy of the products and the total binding energy of the reactants.
$Q = 28.188 \, MeV - 4.448 \, MeV = 23.74 \, MeV$.
Rounding to the nearest provided option,$Q \approx 23.8 \, MeV$.

(B) The binding energy of a nucleus is given by the product of the number of nucleons and the binding energy per nucleon.
For the reactant side, we have two deuterons $(_{1}H^{2})$. Each deuteron has $2$ nucleons. The binding energy of one deuteron is $2x_1$. Since there are two deuterons, the total binding energy of the reactants is $2 \times (2x_1) = 4x_1$.
For the product side, we have one $\alpha$-particle $(_{2}He^{4})$. An $\alpha$-particle has $4$ nucleons. The binding energy of the $\alpha$-particle is $4x_2$.
The energy released $Q$ in a nuclear reaction is equal to the difference between the total binding energy of the products and the total binding energy of the reactants.
Therefore, $Q = (\text{Total Binding Energy of Products}) - (\text{Total Binding Energy of Reactants})$.
$Q = 4x_2 - 4x_1 = 4(x_2 - x_1)$.

(C) The energy released in a nuclear fission reaction is given by the difference between the total binding energy of the products and the total binding energy of the reactants.
Total binding energy of reactants = $236 \times 7.6\, MeV = 1793.6\, MeV$.
Total binding energy of products = $(117 \times 8.5) + (117 \times 8.5) = 234 \times 8.5\, MeV = 1989\, MeV$.
Energy liberated = (Total binding energy of products) - (Total binding energy of reactants).
Energy liberated = $1989\, MeV - 1793.6\, MeV = 195.4\, MeV$.
Rounding to the nearest significant value,the total energy liberated is approximately $200\, MeV$.

(D) The rest mass of a stable nucleus is always less than the sum of the rest masses of its constituent nucleons. This difference is known as the mass defect,$\Delta m$. The energy equivalent to this mass defect,given by $\Delta m c^2$,is the binding energy that keeps the nucleons together.
Nuclear fission is a process in which a very heavy nucleus splits into two or more lighter nuclei,releasing a significant amount of energy.
Nuclear fusion involves the combining of two light nuclei to form a heavier nucleus,not medium-mass nuclei as stated in option $(c)$.
Therefore,both statements $(a)$ and $(b)$ are correct.

(C) Nuclear fission is a process in which a heavy nucleus splits into two lighter nuclei upon bombardment with neutrons.
$U^{235}$ is a fissile isotope,meaning it can undergo fission when hit by slow (thermal) neutrons.
$U^{238}$ is fertile but not fissile with thermal neutrons,as it requires fast neutrons to undergo fission.
Therefore,$_{92}U^{235}$ is the isotope that is normally fissionable.

(B) Control rods are used in nuclear reactors to control the fission rate of uranium and plutonium. They are composed of chemical elements such as boron,silver,indium,and cadmium that are capable of absorbing many neutrons without themselves fissioning.

(A) The process in which a heavy nucleus (such as $ ^{235}U $) splits into two or more lighter nuclei,accompanied by the release of a large amount of energy,is called nuclear fission.
Therefore,the correct option is $A$.

(A) An atomic bomb operates on the principle of uncontrolled nuclear fission.
In this process,a heavy nucleus like $U^{235}$ or $Pu^{239}$ is bombarded with neutrons,causing it to split into smaller nuclei and releasing a massive amount of energy in the form of heat and radiation.
This chain reaction occurs rapidly,leading to a violent explosion.

(C) The energy generation in stars is primarily due to the nuclear fusion of light nuclei,such as hydrogen,into heavier nuclei like helium $(He)$.
In this process,a significant amount of mass is converted into energy according to Einstein's mass-energy equivalence principle,$E = mc^2$,resulting in the release of vast amounts of energy.

(A) Nuclear fusion is a process in which two light nuclei combine to form a heavier nucleus,releasing a large amount of energy.
In the reaction $_1H^2 + _1H^2 \to _2He^4 + 24\;MeV$,two deuterium nuclei fuse to form a helium nucleus.
Therefore,the correct option is $A$.

(D) The nuclear reaction is given by: $_4Be^9 + _2He^4 \rightarrow _6C^{12} + X$.
To find $X$,we balance the mass number and atomic number on both sides.
Sum of mass numbers on the left: $9 + 4 = 13$.
Sum of mass numbers on the right: $12 + A = 13 \implies A = 1$.
Sum of atomic numbers on the left: $4 + 2 = 6$.
Sum of atomic numbers on the right: $6 + Z = 6 \implies Z = 0$.
Since the particle has mass number $1$ and atomic number $0$,it is a neutron,denoted as $_0n^1$.

(B) An atomic bomb operates on the principle of uncontrolled nuclear fission. It consists of two or more pieces of fissile material,such as $_{92}U^{235}$ or $_{94}Pu^{239}$,each of which is smaller than the critical mass. When these pieces are brought together rapidly to form a supercritical mass,a source of neutrons is used to initiate the chain reaction. The neutrons trigger the fission of the uranium or plutonium nuclei,releasing a massive amount of energy.

(D) Nuclear fission is a process in which a heavy nucleus splits into two lighter nuclei. This process is most favorable for heavy nuclei with high atomic numbers,as they are less stable due to the large Coulomb repulsion between protons. Elements with atomic numbers near $92$ (such as Uranium) are highly suitable for nuclear fission because they are heavy and unstable enough to undergo fission upon neutron bombardment. Therefore,the correct option is $D$.

(D) Nuclear reactions occur when nuclei interact to form new products. In the carbon-nitrogen cycle,the reactions $_6C^{12} + _1H^1 \to _7N^{13} + 2 \text{ MeV}$ and $_7N^{14} + _1H^1 \to _8O^{15} + 7.3 \text{ MeV}$ are well-known,experimentally verified nuclear fusion processes that occur in stars. The reaction in option $(a)$ is not a standard nuclear fusion reaction in this context. Therefore,both $(b)$ and $(c)$ are possible nuclear reactions.

(D) Nuclear fusion is a process in which two light atomic nuclei combine to form a single,heavier nucleus. This process is accompanied by the release of a large amount of energy due to the mass defect between the reactants and the product.

(C) In a nuclear reactor,the chain reaction is maintained by neutrons. Cadmium rods are used as control rods because they have a high cross-section for neutron absorption. By inserting or withdrawing these rods,we can control the number of neutrons available for fission,thereby regulating the rate of the chain reaction. Therefore,they are used to absorb some neutrons to maintain a steady state.

(D) Fusion reactions involve the merging of two light nuclei to form a heavier nucleus. Since nuclei are positively charged,they experience a strong electrostatic (Coulomb) repulsion when brought close together. To overcome this repulsion and bring the nuclei within the range of the strong nuclear force,they must possess very high kinetic energy. This high kinetic energy is achieved only at extremely high temperatures (on the order of $10^7 \ K$ to $10^8 \ K$). Therefore,option $D$ is correct.

(C) The hydrogen bomb,also known as a thermonuclear weapon,operates on the principle of uncontrolled nuclear fusion.
Specifically,it involves the fusion of isotopes of hydrogen,namely deuterium $(^2H)$ and tritium $(^3H)$,to form helium $(^4He)$ and a neutron $(n)$,releasing a tremendous amount of energy.
The reaction is represented as: $^2H + ^3H \rightarrow ^4He + n + 17.6 \ MeV$.
Therefore,the correct option is $C$.

(B) The energy produced by the Sun is primarily due to nuclear fusion reactions occurring in its core.
In these reactions,hydrogen nuclei (protons) fuse together to form helium nuclei.
This process releases a tremendous amount of energy in the form of electromagnetic radiation,as the mass of the resulting helium nucleus is slightly less than the sum of the masses of the hydrogen nuclei that fused,with the mass defect being converted into energy according to Einstein's mass-energy equivalence principle,$E = \Delta mc^2$.
Therefore,the correct option is $B$.

(D) The atomic bomb dropped on Nagasaki,Japan,on August $9, 1945$,was codenamed 'Fat Man'.
This bomb utilized a core of Plutonium-$239$ as its primary fissionable material.
In contrast,the bomb dropped on Hiroshima ('Little Boy') used Uranium-$235$.
Therefore,the correct option is $D$.

(C) When fast-moving neutrons pass through a moderator,they collide with the molecules of the moderator.
As a result of these collisions,the neutrons lose kinetic energy until they reach thermal equilibrium with the surrounding molecules of the moderator.
These neutrons,which have kinetic energies comparable to the thermal energy of the surrounding environment (approximately $0.025 \ eV$ at room temperature),are called thermal neutrons.

(B) Fast neutrons are slowed down by passing them through a moderator.
Materials containing light nuclei,such as water $(H_2O)$,heavy water $(D_2O)$,or graphite,are effective moderators.
When a fast neutron collides elastically with a light nucleus (like hydrogen or deuterium),it transfers a significant portion of its kinetic energy to the nucleus,thereby reducing its speed.
Therefore,passing neutrons through water is an effective method to slow them down.

(D) The mass defect $\Delta m$ is $0.1\%$ of the initial mass $m = 1 \, kg$.
$\Delta m = \frac{0.1}{100} \times 1 \, kg = 10^{-3} \, kg$.
Using Einstein's mass-energy equivalence formula,$E = \Delta m c^2$,where $c = 3 \times 10^8 \, m/s$ is the speed of light.
$E = 10^{-3} \, kg \times (3 \times 10^8 \, m/s)^2$.
$E = 10^{-3} \times 9 \times 10^{16} \, J$.
$E = 9 \times 10^{13} \, J$.

(C) Given: Power $P = 1000\, kW = 10^6\, J/s$.
Energy released per fission $E = 200\, MeV = 200 \times 10^6 \times 1.6 \times 10^{-19}\, J = 3.2 \times 10^{-11}\, J$.
The rate of nuclear fission $R$ is given by the ratio of total power to energy per fission:
$R = \frac{P}{E} = \frac{10^6\, J/s}{3.2 \times 10^{-11}\, J/fission}$.
$R = 0.3125 \times 10^{17} = 3.125 \times 10^{16}\, \text{fissions/s}$.

(A) Power $P = 1 \, kW = 1000 \, W = 1000 \, J/s$.
Energy released per fission $E = 200 \, MeV = 200 \times 10^6 \times 1.6 \times 10^{-19} \, J = 3.2 \times 10^{-11} \, J$.
Let $n$ be the number of fissions per second.
The total power produced is $P = n \times E$.
Therefore, $n = P / E$.
$n = 1000 / (3.2 \times 10^{-11}) = 0.3125 \times 10^{14} = 3.125 \times 10^{13} \, \text{fissions per second}$.

(C) In a nuclear fission reaction,a heavy nucleus splits into lighter nuclei and releases energy along with several neutrons. These released neutrons can trigger further fission reactions in other heavy nuclei. This process repeats,creating a self-sustaining chain reaction that continues until the fissile material is exhausted.

(A) In a nuclear fission reaction,both the mass number and the atomic number must be conserved on both sides of the equation.
Given reaction: $_{92}U^{235} + _0n^1 \to _{38}Sr^{90} + X$
Let the unknown product $X$ be $_{Z}A^{A}$.
Conservation of mass number: $235 + 1 = 90 + A \implies 236 = 90 + A \implies A = 146$.
However,the standard fission of $U^{235}$ producing $Sr^{90}$ releases neutrons. Checking the options,option $A$ provides $_{54}Xe^{143} + 3_0n^1$.
Sum of mass numbers: $90 + 143 + 3(1) = 90 + 143 + 3 = 236$.
Sum of atomic numbers: $38 + 54 + 3(0) = 92$.
Since both are conserved,the correct completion is $_{54}Xe^{143} + 3_0n^1$.

(B) Nuclear fusion is a process in which two light nuclei combine to form a heavier nucleus,releasing a large amount of energy.
The reaction of hydrogen isotopes to form helium is a classic example of nuclear fusion,which powers the Sun and stars.
The reaction is given by: $_1H^2 + _1H^2 \to _2He^4 + Q$,where $Q$ is the energy released.

(C) Nuclear fission is typically induced by neutrons because they are electrically neutral and do not experience Coulomb repulsion from the positively charged nucleus.
Fast neutrons are less likely to be captured by the target nucleus $(^{235}U)$ because they pass through the nucleus too quickly.
Slow neutrons (also called thermal neutrons) have a much higher probability of being captured by the target nucleus,which then becomes unstable and undergoes fission.
Therefore,slow neutrons are the most effective projectiles for sustaining a nuclear chain reaction.

(D) The nuclear fusion reaction between two deuterium nuclei $(_{1}H^{2})$ is given by the equation:
$_{1}H^{2} + _{1}H^{2} \to _{1}H^{3} + _{1}H^{1} + Q$
In this reaction,two deuterium nuclei fuse to form a tritium nucleus $(_{1}H^{3})$ and a proton $(_{1}H^{1})$,which is a hydrogen nucleus. Therefore,the correct option is $D$.

(D) $APSARA$ is the name of the first nuclear reactor in India.
It was designed by the Bhabha Atomic Research Center,Mumbai.
It was built with the assistance of the United Kingdom,which also supplied the required uranium.
It was inaugurated on January $20, 1957$.

(B) The mass defect $\Delta m$ is the difference between the initial mass and the final mass.
$\Delta m = 1 \, g - 0.993 \, g = 0.007 \, g = 0.007 \times 10^{-3} \, kg = 7 \times 10^{-6} \, kg$.
According to Einstein's mass-energy equivalence principle,the energy released $E$ is given by $E = \Delta m c^2$,where $c = 3 \times 10^8 \, m/s$ is the speed of light.
$E = (7 \times 10^{-6} \, kg) \times (3 \times 10^8 \, m/s)^2$
$E = 7 \times 10^{-6} \times 9 \times 10^{16} \, J$
$E = 63 \times 10^{10} \, J$.

(A) Thermal neutrons are neutrons with kinetic energy comparable to the thermal energy of the surrounding environment (approximately $0.025 \ eV$).
Fission of $U^{235}$ is induced by thermal neutrons because the binding energy released upon the capture of a neutron by $U^{235}$ is sufficient to overcome the fission barrier.
Other isotopes like $U^{238}$,$Pu^{238}$,and $Th^{232}$ generally require fast neutrons (high kinetic energy) to induce fission.
Therefore,the correct option is $A$.

(C) The nuclear fission reaction of Uranium-$235$ when bombarded by a thermal neutron is represented as:
${ }_{92}^{235} U + { }_{0}^{1} n \rightarrow { }_{54}^{142} Xe + { }_{38}^{90} Sr + 3{ }_{0}^{1} n + Q$
In this specific fission process,one neutron is absorbed to initiate the reaction,and three neutrons are emitted as products.
Therefore,the number of emitted neutrons is $3$.

(B) Power $P = 5 \, W = 5 \, J/s$.
Energy released per fission $E = 200 \, MeV = 200 \times 10^6 \times 1.6 \times 10^{-19} \, J = 3.2 \times 10^{-11} \, J$.
Fission rate $R = \frac{P}{E} = \frac{5}{3.2 \times 10^{-11}} \, s^{-1}$.
$R = 1.5625 \times 10^{11} \, s^{-1} \approx 1.56 \times 10^{11} \, s^{-1}$.

(A) In a typical nuclear fusion reaction,such as the fusion of two deuterium nuclei $(^2H + ^2H \rightarrow ^3He + n + 3.27 \ MeV)$ or the fusion of deuterium and tritium $(^2H + ^3H \rightarrow ^4He + n + 17.6 \ MeV)$,the energy released per reaction is relatively small compared to fission.
However,when considering the energy released per unit mass,fusion is much more efficient.
For a typical fusion reaction involving light nuclei,the energy released is in the range of a few $MeV$ to about $25 \ MeV$.
Therefore,among the given options,$25 \ MeV$ is the most appropriate value for a typical fusion reaction.

(B) The energy in the sun is produced by the process of nuclear fusion,specifically the proton-proton cycle where hydrogen nuclei fuse to form helium. The reaction $_1^1H + _1^1H \to _1^2H + _1^0e + \nu$ is the primary step in this cycle. Among the given options,option $B$ represents a fusion process involving helium isotopes,which is a characteristic of stellar nucleosynthesis.

(D) In a nuclear reactor,fission reactions produce fast-moving neutrons. These fast neutrons have a low probability of causing further fission in $U^{235}$. The function of the moderator (like heavy water,$D_2O$,or graphite) is to collide with these fast neutrons,thereby reducing their kinetic energy through elastic collisions until they reach thermal energies (approximately $0.025 \ eV$). These slow or 'thermal' neutrons are much more effective at inducing fission in $U^{235}$,thus sustaining the chain reaction.

(C) Nuclear fission is a process in which a heavy nucleus,such as $U^{235}$,is bombarded by a neutron,causing it to split into two smaller,lighter nuclei.
This reaction releases a significant amount of energy and,crucially,the emission of several additional neutrons (typically $2$ to $3$ neutrons per fission event).
These released neutrons can then go on to trigger further fission events,sustaining a chain reaction.

(C) To find the particle $X$,we apply the laws of conservation of mass number and atomic number.
Sum of mass numbers on the left side: $1 + 1 + 2 = 4$.
Sum of atomic numbers on the left side: $1 + 1 + 1 = 3$.
Let the particle $X$ be represented as $_Z^A X$.
The reaction is: $_1H^1 + _1H^1 + _1H^2 \to _Z^A X + _{+1}e^0$.
Conservation of mass number: $1 + 1 + 2 = A + 0 \implies A = 4$.
Conservation of atomic number: $1 + 1 + 1 = Z + 1 \implies Z = 2$.
The particle with mass number $4$ and atomic number $2$ is the Helium nucleus,which is an $\alpha$-particle $(_{2}He^4)$.
Thus,the reaction is: $_1H^1 + _1H^1 + _1H^2 \to _2He^4 + _{+1}e^0 + \text{energy}$.

(B) The correct answer is $(b)$. $A$ neutron moderator is a medium that reduces the speed of fast neutrons,thereby turning them into thermal neutrons capable of sustaining a nuclear chain reaction involving uranium$-235$.
Heavy water $(D_2O)$ serves as an effective neutron moderator in a nuclear reactor. It slows down fast-moving neutrons through elastic collisions,which increases the probability of these neutrons causing further fission in uranium nuclei.
Explanation:
In a fission reaction,neutrons are released with high kinetic energy. These fast neutrons are less likely to cause further fission. By using a moderator like heavy water,the neutrons lose kinetic energy and become 'thermal' or 'slow' neutrons,which are much more efficient at sustaining the chain reaction.

(D) The energy in the sun is generated primarily through the process of nuclear fusion.
In the core of the sun,hydrogen nuclei (protons) undergo fusion to form helium nuclei.
This process releases a tremendous amount of energy due to the mass defect between the reactants and the products,as described by Einstein's mass-energy equivalence principle,$E = \Delta mc^2$.

(A) When a slow neutron (thermal neutron) strikes a ${U^{235}}$ nucleus,it is absorbed by the nucleus to form an unstable isotope ${U^{236}}$.
This unstable nucleus immediately undergoes splitting into two lighter nuclei,releasing a large amount of energy and additional neutrons.
This process is known as nuclear fission.
Therefore,the correct process is the fission of ${U^{235}}$.

(A) Nuclear fusion is a process in which two lighter atomic nuclei combine to form a heavier nucleus,releasing a large amount of energy.
In option $A$,two isotopes of hydrogen (deuterium $_1^2H$ and tritium $_1^3H$) fuse to form a helium nucleus $(_{2}^{4}He)$ and a neutron $(_{0}^{1}n)$.
Option $B$ represents radioactive decay (alpha and beta decay).
Option $C$ represents positron emission.
Therefore,the correct reaction representing fusion is $A$.

(C) Nuclear fission is a process in which a heavy nucleus (such as $U-235$) is bombarded by thermal neutrons (low-energy neutrons).
Upon absorption of the neutron,the heavy nucleus becomes unstable and splits into two or more smaller,lighter nuclei,releasing a large amount of energy and additional neutrons.
Therefore,the correct statement is that a heavy nucleus bombarded by thermal neutrons breaks up.

(B) hydrogen bomb operates on the principle of nuclear fusion. In this process,light nuclei,typically isotopes of hydrogen like deuterium and tritium,combine to form a heavier nucleus,releasing a tremendous amount of energy. This is the same process that powers the Sun and stars.

(D) The nuclear fission reaction is represented by the equation: $_{92}U^{235} + _0n^1 \to _{92}U^{236} \to _{56}Ba^{144} + _{36}Kr^{89} + x(_0n^1)$.
To find the number of neutrons $x$,we balance the mass numbers on both sides of the equation.
The sum of mass numbers on the left side is $235 + 1 = 236$.
The sum of mass numbers on the right side is $144 + 89 + x = 233 + x$.
Equating the two sides: $236 = 233 + x$,which gives $x = 3$.
Therefore,$3$ neutrons are released.