Nuclear Fission

Q. The energy equivalent of $0.5\text{g}$ of a substance is :

1. $1.15\times {10}^{13}\text{Joule}$
2. $0.5\times {10}^{13}\text{Joule}$
3. $4.5\times {10}^{16}\text{Joule}$
4. $4.5\times {10}^{13}\text{Joule}$

Q.

The power obtained in a reactor using U²³⁵ disintegration is 1000 kW . What is the mass decay of U²³⁵ per hour ?

Q. Energy released in the fission of a single ${}_{92}{\text{U}}^{235}$ nucleus is $200\text{MeV}$. The fission rate of a ${}_{92}{\text{U}}^{235}$ fuel reactor operating at a power level of $5\text{W}$ is $1.56\times {10}^{5.5k}{\text{s}}^{-1}$. The value of $k$ is -

1. $1$
2. $2$
3. $3$
4. $4$

Q. Consider a binary star system of star $A$ and star $B$ with masses $m_A$ and $m_B$ revolving in a circular orbit of radii $r_A$ and $r_B$, respectively. If $T_A$ and $T_B$ are the time period of star $A$ and star $B$, respectively, then :

1. $T_A>T_B$ (if $m_A>m_B$)
2. $\frac{T_A}{T_B}={\left(\frac{r_A}{r_B}\right)}^{\frac{3}{2}}$
3. $T_A=T_B$
4. $T_A>T_B$ (if $r_A>r_B$)

Q. If one of the two electrons of a $H_2$ Molecule is removed, We get a hydrogen molecular ion $H_2^{+}$. In the ground state of an $H_2^{+}$, the two protons are separated by roughly $1.5A^{\circ }$ and the electron is roughly $1A^{\circ }$ from each proton. Determine the potential energy of the system. Specify your choice of the zero of potential energy.

Q.

Calculate the energy released by 1 g of natural uranium assuming 200 MeV is released in each fission event and that the fissionable isotope ${}^{235}U$ has an abundance of 0.7 % by weight in natural uranium.

Q. $200\text{MeV}$ energy is released when one nucleus of $U^{235}$ undergoes fission. The number of fissions per second required for producing a power of $16\text{MW}$ is-

1. $5\times {10}^{17}$
2. $5\times {10}^{18}$
3. $5\times {10}^{16}$
4. $5\times {10}^{19}$

Q.

The radioactive decay of uranium into thorium is represented by the equation
${}_{92}^{238}U\to {}_{90}^{234}Th+x$
What is x?

1. a neutron

2. an alpha particle

3. an electron

4. a proton

Q. A nucleus of mass number 220 initially at rest emits an alpha particle. If the $Q$ value of the reaction is $5.5MeV$, then the kinetic energy of the alpha particle is

1. $5.5MeV$
2. $5.4MeV$
3. $2.0MeV$
4. $6.5MeV$

Q.

A bomb of 12 kg explodes into two pieces of masses 4 kg and 8 kg. The velocity of 8kg mass is 6 m/sec. The kinetic energy of the other mass is

1. 32 J

2. 24 J

3. 288 J

4. 48 J

Q. In a fission process, nucleus $A$ divides into two nuclei $B$ and $C$, their binding energies being $E_a,E_b$ and $E_c$ respectively. Then

1. $E_b+E_c=E_a$
2. $E_b+E_c>E_a$
3. $E_b+E_c<E_a$
4. $E_b.E_c=E_a$

Q.

The energy released by the fission of one uranium atom is 200 MeV. The number of fissions per second required to produce 3.2 W of power is

1. ${10}^7$

2. ${10}^{10}$

3. ${10}^{15}$

4. ${10}^{17}$

Q. For nuclei with mass number close to 119 and 238, the binding energies per nucleon are approximately 7.6 MeV and 8.6 MeV respectively. If a nucleus of mass number 238 breaks into two nuclei of nearly equal masses, what will be the approximate amount of energy released in the process of fission?

1. 214 MeV
2. 119 MeV
3. 2047 MeV
4. 1142 MeV

Q. An uranium U235 fission reaction produces 216MeV. The amount of U235 required to run a 100MW nuclear power plant for a day with 100% efficiency is (1)0.01kg (2)1kg (3)0.1kg (4)0.001kg

Q. Uranium has two isotopes of masses 235 and 238 units . If both are present in uranium hexafluoride gas which would have the larger average speed ? If atomic mass of fluorine is 19 units , estimate the percentage difference in speeds at any temperature

Q.

${}^{131}I$ is an isotope of Iodine that $\beta -$ decays to an isotope of Xenon with a half-life of $8\text{days}$. A small amount of a serum labelled with ${}^{131}I$ is injected into the blood of a person. The activity of the amount of ${}^{131}I$ injected was $2.4\times {10}^5\text{Becquerel (Bq)}$. It is known that the injected serum will get distributed uniformly in the blood stream in less than half an hour. After $11.5\text{hours},2.5\text{ml}$ of blood is drawn from the person's body, and gives an activity of $115\text{Bq}$. The total volume of blood in the person's body, in $\text{liters}$ is approximately _______.

Q. Find out the mass of Uranium required per day to generate 10 MW power from the fission of 92 U^235

Q. The energy released per fission reaction of ${\text{U}}^{235}$ is $200\text{MeV}$. Find the energy released by the fission of $1\text{g}$ of ${\text{U}}^{235}$.
$(\text{Avogadro number},N_A=6.023\times {10}^{23})$

1. $8.202\times {10}^{14}\text{J}$
2. $8.202\times {10}^{12}\text{J}$
3. $8.202\times {10}^{10}\text{J}$
4. $8.202\times {10}^8\text{J}$

Q. 16. A nucleus disintegrates into two daughter nuclei with masses in the ratio 1:26 if the radius of the parent nucleus is r radius of the lighter daughter nucleus is a) r b) r/2 c) r/3 d) r/9

Q. 15.The half life of radioactive substance is 10 days.What is the time taken for 3/4th of its original mass to disintegrate ?

Q. A nuclear fission is represented by the following reaction

${\text{U}}^{236}\to {\text{X}}^{111}+{\text{Y}}^{122}+3_0{\text{n}}^1$

If the binding energies per nucleon of ${\text{X}}^{111},$ ${\text{Y}}^{122}$ and ${\text{U}}^{236}$ are $8.6\text{MeV},8.5\text{MeV}$$\text{and}7.6\text{MeV}$ respectively, then the energy released in the reaction will be

1. $498\text{MeV}$
2. $398\text{MeV}$
3. $298\text{MeV}$
4. $198\text{MeV}$

Q. In a quark model of elementary particles, a neutron is made of one up quarks [charge $\left(2/3\right)e$] and two down quarks [charges $-\left(1/3\right)e$]. Assume that they have a triangle configuration with side length of the order of ${10}^{–15}m$.

A) Calculate electrostatic potential energy of neutron and compare it with its mass $939MeV$.
B) Calculate electrostatic potential energy of proton and compare it with its mass $939MeV$.

Q. A binary star is a system of two stars rotating about their centre of mass only under mutual gravitational attraction. Let the stars have mass m and $2m$ and let their separation be $l$. Their time period of rotation about their centre of mass will be proportional to

1. $l^2$
2. $l^{3/2}$
3. $l^{1/2}$
4. $l$

Q. A nuclear fission is given below
$A^{240}\to B^{100}+C^{140}+Q\left(\text{energy}\right)$.
Let binding energy per nucleon of nucleus $A,B$ and $C$ is $7.6\text{MeV},8.1\text{MeV}$ and $8.1\text{MeV}$ respectively. Value of $Q$ is : (Approximately)

1. $20\text{MeV}$
2. $220\text{MeV}$
3. $120\text{MeV}$
4. $240\text{MeV}$

Q. In a fission reaction ${}_{92}^{236}U{\to }^{117}X{+}^{117}Y+n+n$, the binding energy per nucleon of X and Y is 8.5 MeV whereas of 236 U is 7.6 MeV. The total energy liberated will be about

1. 200 KeV
2. 2 MeV
3. 200 MeV
4. 2000 MeV

Q. After a certain lapse of time, the fraction of radioactive polonium undecayed is found to be $12.5\%$ of initial quantity. The duration of this time-lapse is, (if the half-life of polonium is $138$ days)

1. $407$ days
2. $410$ days
3. $421$ days
4. $414$ days

Q. A radioactive element ${}_{92}^{235}X$ is bombarded with a neutron, it generates ${}_{36}^{89}Y$, three neutrons and ${}_{56}^{A}Z.$The value of $A$ is

1. $140$
2. $148$
3. $144$
4. $142$

Q. When a ${}_{92}^{235}\text{U}$ isotope is bombarded with a neutron it generates ${}_{51}^{133}\text{Sb}$, four neutrons and

1. ${}_{38}^{94}\text{Sr}$
2. ${}_{54}^{140}\text{Xe}$
3. ${}_{41}^{99}\text{Nb}$
4. ${}_{36}^{89}\text{Kr}$

Q. In the nuclear fusion reaction,

${}_1{\text{H}}^2{+}_1{\text{H}}^3{\to }_2{\text{He}}^4{+}_0{n}^1$

The repulsive potential energy between the two fusing nuclei is $7.7\times {10}^{-14}\text{J}$. The temperature to which the gas must be heated is nearly
$(\text{Boltzmen constant}K=1.38\times {10}^{-23}{\text{JK}}^{-1})$

1. ${10}^3\text{K}$
2. $3.7\times {10}^5\text{K}$
3. ${10}^7\text{K}$
4. $3.7\times {10}^9\text{K}$

Q. Complete the equation for the following fission process
${}_{92}{\text{U}}^{235}{+}_0{n}^1\to {}_{38}{\text{Sr}}^{90}+\text{\_\_\_\_\_}$

1. ${}_{57}{X}^{142}+3_0{n}^1$
2. ${}_{54}{X}^{145}+3_0{n}^1$
3. ${}_{54}{X}^{143}+3_0{n}^1$
4. ${}_{54}{X}^{142}+{}_0{n}^1$