Mechanism of Nuclear Fission

Q. The binding energy per nucleon of ${}_3^7\text{Li}$ and ${}_2^4\text{He}$ nuclei are $5.60\text{MeV}$ and $7.06\text{MeV}$, respectively. In the nuclear reaction ${}_3^7\text{Li}{+}_1^1\text{H}\to {}_2^4\text{He}+Q,$ the value of energy $Q$ released is

1. $19.6\text{MeV}$
2. $-2.4\text{MeV}$
3. $8.4\text{MeV}$
4. $17.3\text{MeV}$

Q. Consider the nuclear fission ${\text{Ne}}^{20}\to 2{\text{He}}^{+}+{\text{C}}^{12}$.
Given that the binding energy/nucleon of ${\text{Ne}}^{20},{\text{He}}^{+}{\text{and C}}^{12}$ are $8.03\text{MeV},7.07\text{MeV and}7.86\text{MeV}$ respectively. Identify the correct statement

1. Energy of $12.4\text{MeV}$ will be supplied
2. $8.3\text{MeV}$ energy will be released
3. Energy of $3.6\text{MeV}$ will be released
4. Energy of $9.72\text{MeV}$ has to be supplied

Q. The binding energy per nucleon for a deuteron and an alpha particle, are $x_1$ and $x_2$ respectively. What will be the energy released in the following reaction?
${}_1{H}^2+{}_1{H}^2\to {}_{2}H{e}^4$

1. $4(x_1+x_2)$
2. $4(x_2-x_1)$
3. $2(x_1+x_2)$
4. $2(x_2-x_1)$

Q. Consider the nuclear reaction $X^{200}\to A^{110}+B^{80}.$ If the binding energy per nucleon for $X,A$ and $B$ are $7.4\text{MeV},8.2\text{MeV}$ and $8.1\text{MeV}$ respectively, then the energy released in the reaction is

1. $70\text{MeV}$
2. $200\text{MeV}$
3. $190\text{MeV}$
4. $10\text{MeV}$

Q. The value of binding energy per nucleon is

1. Equal for all nuclei
2. More for light nuclei
3. More for medium nuclei
4. More for heavy nuclei

Q. The nuclear force is attractive for separation distance -

1. $=0.8\text{fm}$
2. $<0.8\text{fm}$
3. $>0.8\text{fm}$
4. None of these

Q. The incorrect statement about binding energy is

1. It is the energy required to break a given nucleus into its free nucleons.
2. It is the sum of the rest mass energies of the nucleons minus the rest mass energy of the nucleus.
3. It is the energy required to bind the free nucleons to form a nucleus.
4. It is the energy released when the free nucleons combine to form a nucleus.

Q. Consider the nuclear reaction,

${\text{X}}^{200}\to {\text{A}}^{110}+{\text{B}}^{90}$

If the binding energy per nucleon for $\text{X},\text{A}$ and $\text{B}$ is $7.4\text{MeV},8.2\text{MeV}$ and $8.2\text{MeV}$ respectively, what is the energy released?

1. $200\text{MeV}$
2. $90\text{MeV}$
3. $110\text{MeV}$
4. $160\text{MeV}$

Q. The total binding energy of an a particle ${(}_{2}H{e}_4)$ is $24.4\text{MeV}$ whereas the total binding energy of a deuteron ${(}_1{H}^2)$ is $2.2\text{MeV}$ When two deuterons are made to combine

1. An amount of $22.2\text{MeV}$ energy will be released
2. An amount of $20.0\text{MeV}$ energy will be released
3. An amount of $20.0\text{MeV}$ energy will be consumed
4. An amount of $22.2\text{MeV}$ energy will be consumed

Q. What is the maximum value of binding energy per nucleon ?

1. 8 MeV
2. 8.8 MeV
3. 7.6 MeV
4. 1.1 MeV

Q. Consider the nuclear reaction
$X^{200}\to A^{110}+B^{90}$
If the binding energy per nucleon for $X,A$ and $B$ are $7.4\text{MeV},8.2\text{MeV}$ and $8.2\text{MeV}$ respectively, the energy released in the reaction is

1. $160\text{MeV}$
2. $110\text{MeV}$
3. $200\text{MeV}$
4. $90\text{MeV}$

Q.

The binding energy of deuteron ${(}_1^{2}H)$ is 1.15 MeV per nucleon and an alpha particle ${(}_2^{4}He)$ has a binding energy of 7.1 MeV per nucleon. Then in the reaction
${}_1^{2}H{+}_1^{2}H{\to }_2^{4}He+Q$
the energy Q released is

1. 1 MeV

2. 11.9 MeV

3. 23. MeV

4. 931 MeV

Q. Binding energy per nucleon for $C^{12}$ is 7.68 MeV and for $C^{13}$ is $7.74MeV$. The energy required to remove a neutron from $C^{13}$ is

1. $8.46MeV$
2. $5.49MeV$
3. $9.45MeV$
4. $15.49MeV$

Q. The binding energy per nucleus of ${}_1^{7}Li$ and ${}_2^{4}He$ nuclei are $5.60MeV$ and $7.06MeV$ respectively. In the nucleus reaction ${}_3^{7}Li{+}_1^{1}He{+}_2^{4}He+Q$ the value of energy $Q$ released is:

1. $-2.4MeV$
2. $8.4MeV$
3. $19.6MeV$
4. $17.3MeV$

Q. This section contains 1 Assertion-Reason type question, which has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
A : Rate constant of reactions which have low activation energy are more sensitive towards change in temperature as compared to that of reactions with high activation energy.
R : Lower the activation energy faster the reaction.

इस खण्ड में 1 कथन-कारण प्रकार का प्रश्न है, जिसमें 4 विकल्प (A), (B), (C) तथा (D) दिये गये हैं, जिनमें से केवल एक सही है।
A : निम्‍न सक्रियण ऊर्जा वाली अभिक्रियाओं का वेग नियतांक ताप में परिवर्तन के प्रति उच्च सक्रियण ऊर्जा वाली अभिक्रियाओं की तुलना में अधिक संवेदी होता है।
R : सक्रियण ऊर्जा कम होने पर अभिक्रिया तीव्रता से होती है।

1. (A) is true but (R) is false
   (A) सही है लेकिन (R) गलत है
2. Both (A) and (R) are true and (R) is the correct explanation of (A)
   (A) तथा (R) दोनों सही हैं तथा (R), (A) का सही स्पष्टीकरण है
3. (A) is false but (R) is true
   (A) गलत है लेकिन (R) सही है
4. Both (A) and (R) are true but (R) is not the correct explanation of (A)
   (A) तथा (R) दोनों सही हैं लेकिन (R), (A) का सही स्पष्टीकरण नहीं है

Q. A $1000MW$ fission reactor consumes half of its fuel in $5.00y$. How much ${}_{92}^{235}U$ did it contain initially? Assume that the reactor operates $80\%$ of the time, that all the energy generated arises from the fission of ${}_{92}^{235}U$ and that this nuclide is consumed only by the fission process.

Q. Shown here are the steps of nuclear fission using the liquid drop model. Which of these is the correct sequence?

1. b, c, a
2. a, b, c
3. c, b, a
4. b, a, c

Q. The binding energy per nucleon for a $\text{deuteron}$ and an $\alpha -\text{particle}$ is $x_1$ and $x_2$ respectively. The energy $Q$ released in the reaction ${}_1{\text{H}}^2{+}_1{\text{H}}^2{\to }_2{\text{He}}^4+Q,$ is

1. $4(x_1+x_2)$
2. $4(x_2-x_1)$
3. $2(x_2-x_1)$
4. $2(x_1+x_2)$

Q. Assume a hypothetical nuclear fission reaction:
$X\to Y+Z$
If the atomic masses of $X,Y\&Z$ are respectively $x,y\&z$ calculate the maximum amount of heat generated if 1 gram of X undergoes fission. Consider the molar mass of X to be M.

1. 
2. 
3. 
4. 

Q. Shown here are the steps of nuclear fission using the liquid drop model. Which of these is the correct sequence?

1. b, c, a
2. c, b, a
3. a, b, c
4. b, a, c

Q. Obtain the binding energy of the nuclei ${}_{26}^{56}Fe$ and ${}_{83}^{209}Bi$ in units of MeV from the following data:
(a) $m{(}_{26}^{56}Fe)=55.934939u$
(b) $m{(}_{83}^{209}Bi)=208.980388u$

Q. The binding energy per nucleon of a Deuteron $\left({}_1^{2}H\right)$ and helium nucleus $\left({}_2^{4}He\right)$ is $1.1MeV$ and $7MeV$ respectively. If two deuteron nuclei react to form a single helium nucleus, then the energy released is :

1. $19.2MeV$
2. $13.9MeV$
3. $26.9MeV$
4. $23.6MeV$

Q. The following figure represents the liquid drop model of nuclear fission. The energies of these states are $E_1$, $E_2$ and $E_3$respectively. Which option is correct?

1. >>
2. ><
3. <>
4. <<

Q. What parameter is used to measure the stability of a nucleus?

1. Average binding energy
2. No. of neutrons
3. No. of protons
4. No. of electrons

Q. The above is a plot of binding energy per nucleon $E_b,$ against the nuclear mass M; A, B, C, D, E, correspond to different nuclei. Consider four reactions :
(i) $A+B\to C+\epsilon$
(ii) $C\to A+B+\epsilon$
(iii) $D+E\to F+\epsilon$
(iv) $F\to D+E+\epsilon ,$
where $\epsilon$ is the energy released. In which reactions $\epsilon$ positive?

1. (i) and (iii)
2. (ii) and (iv)
3. (i) and (iv)
4. (ii) and (iii)

Q. Shown here are the steps of nuclear fission using the liquid drop model. Which of these is the correct sequence?

1. b, c, a
2. c, b, a
3. a, b, c
4. b, a, c

Q. The following figure represents the liquid drop model of nuclear fission. The energies of these states are $E_1$, $E_2$ and $E_3$respectively. Which option is correct?

1. $E_1$>$E_2$>$E_3$
2. $E_1$>$E_2$<$E_3$
3. $E_1$<$E_2$>$E_3$
4. $E_1$<$E_2$<$E_3$

Q. The binding energy per nucleon for $C^{12}$ is $7.68\text{MeV}$ and that for $C^{13}$ is $7.5\text{MeV}$. The energy required to remove a neutron from $C^{13}$ is

1. $5.34\text{MeV}$
2. $5.5\text{MeV}$
3. $9.5\text{MeV}$
4. $9.34\text{MeV}$

Q.

The root mean square velocity of helium molecules at NTP will be :

1. 0.5 x 10${}^5$ m/s
2. 1.3 x 10${}^3$ m/s
3. 1.5 x 10${}^6$ m/s
4. 1.5 x 10${}^7$ m/s

Q. Statement I: Nuclear fission is not a spontaneous process as the energy is required to be supplied to it to reach the intermediate state before breaking up into two fragments.
Statement II: The energy of the intermediate state is higher than the initial energy of the parent nucleus.

1. Both the statements are correct but statement II doesn’t infer to statement I
2. Both the statements are correct and statement II infers to statement I
3. Statement I is correct but statement II is incorrect
4. Statement II is correct but statement I is incorrect