Nuclear Fission, Fusion and Nuclear Reactor Questions in English

$A$ nucleus ${}^{220}X$ at rest decays by emitting an $\alpha$-particle. If the kinetic energy of the daughter nucleus is $0.2 \, MeV$,the $Q$-value of the reaction is ........ $MeV$.

$A$ certain stable nuclide,after absorbing a neutron,emits a $\beta$-particle and the new nuclide splits spontaneously into two $\alpha$-particles. The nuclide is

For the nuclear fusion reaction ${ }_1^2 H +{ }_1^3 H \rightarrow{ }_2^4 He +{ }_0^1 n$,the temperature to which the gases must be heated is $3.7 \times 10^9 \, K$. The potential energy between two nuclei is closest to ........ $J$ (Boltzmann's constant $k = 1.38 \times 10^{-23} \, J/K$).

In the proton-proton cycle, four hydrogen nuclei combine to release energy of ....... $MeV$.

The energy released per fission of a nucleus of ${}^{240}X$ is $200 \ MeV$. The energy released if all the atoms in $120 \ g$ of pure ${}^{240}X$ undergo fission is $........ \times 10^{25} \ MeV$. (Given $N_A = 6 \times 10^{23}$)

In a nuclear fission process,a high mass nuclide $(A \approx 236)$ with binding energy $7.6 \ MeV/\text{nucleon}$ dissociates into two middle mass nuclides $(A \approx 118)$,each having a binding energy of $8.6 \ MeV/\text{nucleon}$. The energy released in the process is $MeV$.

The explosive in a Hydrogen bomb is a mixture of ${ }_1 H^2, { }_1 H^3$ and ${ }_3 Li^6$ in some condensed form. The chain reaction is given by:
${ }_3 Li^6 + { }_0 n^1 \rightarrow { }_2 He^4 + { }_1 H^3$
${ }_1 H^2 + { }_1 H^3 \rightarrow { }_2 He^4 + { }_0 n^1$
During the explosion,the energy released is approximately:
[Given: $M(Li^6) = 6.01690 \ amu, M({ }_1 H^2) = 2.01471 \ amu, M({ }_2 He^4) = 4.00388 \ amu$,and $1 \ amu = 931.5 \ MeV$] (in $MeV$)

In a nuclear fission reaction of an isotope of mass $M$,three similar daughter nuclei of the same mass are formed. The speed of a daughter nucleus in terms of mass defect $\Delta M$ will be:

Which of the following nuclear fragments corresponding to nuclear fission between a neutron $\left({ }_{0}^{1} n\right)$ and a uranium isotope $\left({ }_{92}^{235} U\right)$ is correct?

The disintegration energy $Q$ for the nuclear fission of ${ }^{235} U \rightarrow{ }^{140} Ce+{ }^{94} Zr+n$ is $\_ \text{MeV}$.
Given atomic masses of:
${ }^{235} U: 235.0439 \text{ u}, { }^{140} Ce: 139.9054 \text{ u},$
${ }^{94} Zr: 93.9063 \text{ u}, n: 1.0086 \text{ u},$
Value of $c^2 = 931 \text{ MeV/u}$.

If three helium nuclei combine to form a carbon nucleus,then the energy released in this reaction is $\times 10^{-2} \text{ MeV}$. (Given $1 \text{ u} = 931 \text{ MeV}/c^2$,atomic mass of helium $= 4.002603 \text{ u}$,atomic mass of carbon $= 12.000000 \text{ u}$)

In a hypothetical fission reaction
${ }_{92} X^{236} \rightarrow{ }_{56} Y^{141}+{ }_{36} Z^{92}+3 R$
The identity of emitted particles $(R)$ is :

$A$ star has $100 \%$ helium composition. It starts to convert three ${ }^4 He$ into one ${ }^{12} C$ via the triple alpha process as ${ }^4 He + { }^4 He + { }^4 He \rightarrow { }^{12} C + Q$. The mass of the star is $2.0 \times 10^{32} \ kg$ and it generates energy at the rate of $5.808 \times 10^{30} \ W$. The rate of converting these ${ }^4 He$ nuclei to ${ }^{12} C$ is $n \times 10^{42} \ s^{-1}$,where $n$ is. . . . . . . [Take,mass of ${ }^4 He = 4.0026 \ u$,mass of ${ }^{12} C = 12 \ u$,$1 \ u = 1.66 \times 10^{-27} \ kg$,$c = 3 \times 10^8 \ m/s$]

The energy released in the fusion of $2 \ kg$ of hydrogen deep in the sun is $E_{H}$ and the energy released in the fission of $2 \ kg$ of ${ }^{235} U$ is $E_U$. The ratio $\frac{E_H}{E_U}$ is approximately :
(Consider the fusion reaction as $4{ }_1^1 H + 2 e^{-} \rightarrow { }_2^4 He + 2 \nu + 6 \gamma + 26.7 \ MeV$,energy released in the fission reaction of ${ }^{235} U$ is $200 \ MeV$ per fission nucleus and $N_{A} = 6.023 \times 10^{23}$ )

In the options given below, let $E$ denote the rest mass energy of a nucleus and $n$ a neutron. The correct option is:

Scientists are working hard to develop a nuclear fusion reactor. Nuclei of heavy hydrogen,${ }_1^2 H$,known as deuteron and denoted by $D$,can be thought of as a candidate for a fusion reactor. The $D-D$ reaction is ${ }_1^2 H+{ }_1^2 H \rightarrow{ }_2^3 He+n+$ energy. In the core of a fusion reactor,a gas of heavy hydrogen is fully ionized into deuteron nuclei and electrons. This collection of ${ }_1^2 H$ nuclei and electrons is known as plasma. The nuclei move randomly in the reactor core and occasionally come close enough for nuclear fusion to take place. Usually,the temperatures in the reactor core are too high and no material wall can be used to confine the plasma. Special techniques are used which confine the plasma for a time $t_0$ before the particles fly away from the core. If $n$ is the density (number/volume) of deuterons,the product $n t_0$ is called the Lawson number. In one of the criteria,a reactor is termed successful if the Lawson number is greater than $5 \times 10^{14} \, s/cm^3$.
It may be helpful to use the following: Boltzmann constant $k=8.6 \times 10^{-5} \, eV/K$; $\frac{e^2}{4 \pi \varepsilon_0}=1.44 \times 10^9 \, eV \cdot m$.
$1.$ In the core of a nuclear fusion reactor,the gas becomes plasma because of
$(A)$ strong nuclear force acting between the deuterons
$(B)$ Coulomb force acting between the deuterons
$(C)$ Coulomb force acting between deuteron-electron pairs
$(D)$ the high temperature maintained inside the reactor core
$2.$ Assume that two deuteron nuclei in the core of a fusion reactor at temperature $T$ are moving towards each other,each with kinetic energy $1.5 kT$,when the separation between them is large enough to neglect Coulomb potential energy. Also,neglect any interaction from other particles in the core. The minimum temperature $T$ required for them to reach a separation of $4 \times 10^{-15} \, m$ is in the range
$(A)$ $1.0 \times 10^9 \, K$ $(B)$ $2.0 \times 10^9 \, K$ $(C)$ $3.0 \times 10^9 \, K$ $(D)$ $4.0 \times 10^9 \, K$
$3.$ Results of calculations for four different designs of a fusion reactor using $D-D$ reaction are given below. Which of these is most promising based on the Lawson criterion?
$(A)$ deuteron density $=2.0 \times 10^{12} \, cm^{-3}$,confinement time $=5.0 \times 10^{-3} \, s$
$(B)$ deuteron density $=8.0 \times 10^{14} \, cm^{-3}$,confinement time $=9.0 \times 10^{-1} \, s$
$(C)$ deuteron density $=4.0 \times 10^{23} \, cm^{-3}$,confinement time $=1.0 \times 10^{-11} \, s$
$(D)$ deuteron density $=1.0 \times 10^{24} \, cm^{-3}$,confinement time $=4.0 \times 10^{-12} \, s$
Give the answer for questions $1, 2,$ and $3.$

The isotope ${}_{5}^{12}B$ having a mass $12.014 \text{ u}$ undergoes $\beta$-decay to ${}_{6}^{12}C$. ${}_{6}^{12}C$ has an excited state of the nucleus $({}_{6}^{12}C^*)$ at $4.041 \text{ MeV}$ above its ground state. If ${}_{5}^{12}B$ decays to ${}_{6}^{12}C^*$, the maximum kinetic energy of the $\beta$-particle in units of $\text{MeV}$ is ($1 \text{ u} = 931.5 \text{ MeV}/c^2$, where $c$ is the speed of light in vacuum).

Suppose a ${ }_{88}^{226} Ra$ nucleus at rest and in the ground state undergoes $\alpha$-decay to a ${ }_{86}^{222} Rn$ nucleus in its excited state. The kinetic energy of the emitted $\alpha$ particle is found to be $4.44 \text{ MeV}$. The ${ }_{86}^{222} Rn$ nucleus then goes to its ground state by $\gamma$-decay. The energy of the emitted $\gamma$-photon is . . . . . . . $\text{keV}$.
[Given: atomic mass of ${ }_{88}^{226} Ra = 226.005 \text{ u}$,atomic mass of ${ }_{86}^{222} Rn = 222.000 \text{ u}$,atomic mass of $\alpha$ particle $= 4.000 \text{ u}$,$1 \text{ u} = 931 \text{ MeV}/c^2$]

The mass of a nucleus ${ }_Z^A X$ is less than the sum of the masses of $(A-Z)$ neutrons and $Z$ protons. The energy equivalent to this mass difference is the binding energy. $A$ heavy nucleus of mass $M$ can break into two light nuclei of masses $m_1$ and $m_2$ only if $M > (m_1+m_2)$. The masses of some neutral atoms are given in the table below:

${ }_1^1 H$: $1.007825 u$	${ }_1^2 H$: $2.014102 u$	${ }_1^3 H$: $3.016050 u$	${ }_2^4 He$: $4.002603 u$
${ }_3^6 Li$: $6.015123 u$	${ }_3^7 Li$: $7.016004 u$	${ }_{30}^{70} Zn$: $69.925325 u$	${ }_{34}^{82} Se$: $81.916709 u$
${ }_{64}^{152} Gd$: $151.919803 u$	${ }_{82}^{206} Pb$: $205.974455 u$	${ }_{83}^{209} Bi$: $208.980388 u$	${ }_{84}^{210} Po$: $209.982876 u$

$1.$ The correct statement is:
$(A)$ The nucleus ${ }_3^6 Li$ can emit an alpha particle.
$(B)$ The nucleus ${ }_{84}^{210} Po$ can emit a proton.
$(C)$ Deuteron $({ }_1^2 H)$ and alpha particle $({ }_2^4 He)$ can undergo complete fusion.
$(D)$ The nuclei ${ }_{30}^{70} Zn$ and ${ }_{34}^{82} Se$ can undergo complete fusion.
$2.$ The kinetic energy (in $keV$) of the alpha particle, when the nucleus ${ }_{84}^{210} Po$ at rest undergoes alpha decay, is:
$(A)$ $5319$ $(B)$ $5422$ $(C)$ $5707$ $(D)$ $5818$

Match the nuclear processes given in column $I$ with the appropriate option$(s)$ in column $II$.

Column $I$	Column $II$
$A$. Nuclear fusion	$P$. Absorption of thermal neutrons by ${}_{92}^{235}U$
$B$. Fission in a nuclear reactor	$Q$. ${}_{27}^{60}Co$ nucleus
$C$. $\beta$-decay	$R$. Energy production in stars via hydrogen conversion to helium
$D$. $\gamma$-ray emission	$S$. Heavy water
	$T$. Neutrino emission

$A$ fission reaction is given by ${ }_{92}^{236} U \rightarrow{ }_{54}^{140} Xe +{ }_{38}^{94} Sr + x + y$,where $x$ and $y$ are two particles. Considering ${ }_{92}^{236} U$ to be at rest,the kinetic energies of the products are denoted by $K_{Xe}, K_{Sr}, K_x (2 \ MeV)$ and $K_y (2 \ MeV)$,respectively. Let the binding energies per nucleon of ${ }_{92}^{236} U, { }_{54}^{140} Xe$ and ${ }_{38}^{94} Sr$ be $7.5 \ MeV, 8.5 \ MeV$ and $8.5 \ MeV$ respectively. Considering different conservation laws,the correct option$(s)$ is(are):

$A$ heavy nucleus $N$,at rest,undergoes fission $N \rightarrow P+Q$,where $P$ and $Q$ are two lighter nuclei. Let $\delta=M_N-M_P-M_Q$,where $M_P, M_Q$ and $M_N$ are the masses of $P, Q$ and $N$,respectively. $E_P$ and $E_Q$ are the kinetic energies of $P$ and $Q$,respectively. The speeds of $P$ and $Q$ are $v_P$ and $v_Q$,respectively. If $c$ is the speed of light,which of the following statement$(s)$ is(are) correct?
$(A)$ $E_P+E_Q=c^2 \delta$
$(B)$ $E_P=\left(\frac{M_P}{M_P+M_Q}\right) c^2 \delta$
$(C)$ $\frac{v_P}{v_Q}=\frac{M_Q}{M_P}$
$(D)$ The magnitude of momentum for $P$ as well as $Q$ is $c \sqrt{2 \mu \delta}$,where $\mu=\frac{M_P M_Q}{M_P+M_Q}$

The minimum kinetic energy needed by an alpha particle to cause the nuclear reaction ${ }_{7}^{16} N +{ }_{2}^{4} He \rightarrow{ }_{1}^{1} H +{ }_{8}^{19} O$ in a laboratory frame is $n$ (in $MeV$). Assume that ${ }_{7}^{16} N$ is at rest in the laboratory frame. The masses of ${ }_{7}^{16} N, { }_{2}^{4} He, { }_{1}^{1} H$ and ${ }_{8}^{19} O$ can be taken to be $16.006 \ u, 4.003 \ u, 1.008 \ u$ and $19.003 \ u$,respectively,where $1 \ u = 930 \ MeV/c^2$. The value of $n$ is. . . . .

Energy released when two deuterons $\left({ }_1 H ^2\right)$ fuse to form a helium nucleus $\left({ }_2 He ^4\right)$ is $:$
(Given $:$ Binding energy per nucleon of ${ }_1 H ^2=1.1 \ \text{MeV}$ and binding energy per nucleon of ${ }_2 He ^4=7.0 \ \text{MeV}$) (in $\text{MeV}$)

Match the $\text{LIST-I}$ with $\text{LIST-II}$:

$A. \text{ } _0^1 n + { }_{92}^{235} U \rightarrow { }_{54}^{140} Xe + { }_{38}^{94} Sr + 2_0^1 n$	$I. \text{ Chemical reaction}$
$B. \text{ } 2H_2 + O_2 \rightarrow 2H_2O$	$II. \text{ Fusion with } +ve \ Q \text{ value}$
$C. \text{ } _1^2 H + _1^2 H \rightarrow _2^3 He + _0^1 n$	$III. \text{ Fission}$
$D. \text{ } _1^1 H + _1^3 H \rightarrow _1^2 H + _1^2 H$	$IV. \text{ Fusion with } -ve \ Q \text{ value}$

Choose the correct answer from the options given below:

Let $E_1$ and $E_2$ be the binding energies of two nuclei $A$ and $B.$ It is observed that two nuclei of $A$ combine together to form a $B$ nucleus. This observation is correct only if

An atomic power nuclear reactor can deliver $300\ MW$. The energy released due to fission of each nucleus of uranium atom $^{238}U$ is $170\ MeV$. The number of uranium atoms fissioned per hour will be:

Energy released in the fission of a single ${ }_{92} U^{235}$ nucleus is $200 \ MeV$. The fission rate of a ${ }_{92} U^{235}$ fuelled reactor operating at a power level of $32 \ kW$ is:

Pick out the unmatched pair from the following $:-$

Find the value of $x$ and $y$ in the following nuclear reaction:
${}_{92}^{235} U + {}_{0}^{1} n \rightarrow {}_{x}^{133} Sb + {}_{41}^{y} Nb + 4 {}_{0}^{1} n$

In the proton-proton cycle in the Sun,the energy released when an electron and its antiparticle combine is $\qquad$ .

The energy of the fast neutrons emitted in a nuclear fission reactor is approximately $\qquad$ .

The energy released by the fission of one uranium atom is $200 \text{ MeV}$. The number of fissions per second required to produce $6.4 \text{ W}$ power is $\qquad$ .

The energy released in the explosion of an atom bomb is mainly due to $\qquad$ .

In the given nuclear reaction
${ }_{4}^{9} Be+{ }_{2}^{4} He \rightarrow{ }_{6}^{12} C+X$
$X$ represents $\qquad$

Complete the following nuclear reaction:
${ }_{0}^{1} n+{ }_{92}^{235} U \rightarrow{ }_{92}^{236} U \rightarrow$ $\qquad$ $+{ }_{41}^{99} Nb+$ $\qquad$.

Choosing the correct option, complete the given nuclear fusion reaction that occurs in the sun.
${ }_1^3 H +{ }_1^3 H \rightarrow{ }_2^4 He +{ }_1^1 H +{ }_1^1 H +$ . . . . . . . (in $\text{ MeV}$)

One of the fusion reactions in the sun is given by ${ }_{1}^{2} H+{ }_{1}^{1} H \rightarrow{ }_{2}^{3} He+\gamma+Q$. Calculate the energy $Q$ released in the reaction. (in $MeV$)

Consider the nuclear fission reaction ${ }_0^1 n+{ }_{92}^{235} U \longrightarrow{ }_{56}^{144} Ba+{ }_{36}^{89} Kr+3{ }_0^1 n$. Assuming all the kinetic energy is carried away by the fast neutrons only and total binding energies of ${ }_{92}^{235} U, { }_{56}^{144} Ba$ and ${ }_{36}^{89} Kr$ to be $1800 \ MeV, 1200 \ MeV$ and $780 \ MeV$ respectively,the average kinetic energy carried by each fast neutron is (in $MeV$):

$A$ nucleus with mass number $220$ initially at rest emits an alpha particle. If the $Q$ value of the reaction is $5.5 \ MeV$,calculate the kinetic energy of the alpha particle. (in $MeV$)

The binding energy per nucleon of deuteron $({ }_{1} H^{2})$ and the helium atom $({ }_{2} He^{4})$ are $1.1 \ MeV$ and $7 \ MeV$ respectively. If two deuteron nuclei fuse to form a single helium nucleus,then the energy released is: (in $MeV$)

$A$ nuclear reactor delivers a power of $10^9 \,W$. The amount of fuel consumed by the reactor in one hour is: (in $\,g$)

In a nuclear reactor,heavy nuclei are not used as moderators because:

The thermonuclear reaction of hydrogen inside the stars takes place by a cycle of operations. The particular element which acts as a catalyst is

The phenomenon in which a proton flips is

On bombarding $U^{235}$ by slow neutrons,$200 \text{ MeV}$ of energy is released. If the power output of an atomic reactor is $1.6 \text{ MW}$,then the rate of fission will be:

In a nuclear reactor,the function of the moderator is to decrease

Pick out the correct statements from the following:
$I$. Electron emission during $\beta$-decay is always accompanied by neutrino.
$II$. Nuclear force is charge independent.
$III$. Fusion is the chief source of stellar energy.

Which one of the following is not correct?

Each nuclear fission of ${}^{235}U$ releases $200 \text{ MeV}$ of energy. If a reactor generates $1 \text{ MW}$ power,then the rate of fission in the reactor is: