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Multiple choice nuclear reactions nuclear structure nuclei atomic nuclei physics

The mass defect in a particular nuclear reaction in 0.3 grams.The amount of energy liberated in kilowatt hour is $\left( Velocity\ of \  light=3\times { 10 }^{ 8 }m/s \right) $

  1. $1.5\times { 10 }^{ 6 }$

  2. $2.5\times { 10 }^{ 6 }$

  3. $3\times { 10 }^{ 6 }$

  4. $7.5\times { 10 }^{ 6 }$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Mass defect in a nuclear reaction          $\Delta M = 0.3    g  =  3 \times 10^{-4}    kg$

Thus amount of energy released        $E = \Delta M    c^2  =  (3 \times 10^{-4}) \times (3 \times 10^8)^2           J$
$\implies         E =  27  \times 10^{12}      J                                  (1   kWh = 3.6  \times 10^6    J)$
$\therefore         E  = 7.5   \times 10^{6}     kWh $

Multiple choice nuclear reactions nuclear structure nuclei atomic nuclei physics

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

  1. $5.34MeV$

  2. $5.5MeV$

  3. $9.5 MeV$

  4. $9.34MeV$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total B.E. for $C^{13}$ is $13\times7.5=97.5\ MeV$

Total B.E. for $C^{12}$ is $12\times7.68=92.16\ MeV$
The energy required to remove a neutron from $C^{13}$ is $97.5-92.16=5.34\ MeV$

Multiple choice nuclear reactions nuclear structure nuclei atomic nuclei physics

When a neutron collides with a quasi free proton, it loses half of its energy on the average in the every collission. How many collisions, on the average, are required to reduce a 2 MeV neutron to a thermal energy df 0.04 eV.

  1. 30

  2. 22

  3. 35

  4. 26
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let $E _{0}$ be the initial energy of neutron, the energy of neutron after 1 collision reduces to $E _{0}/2=E _{1}(let)$ i.e. $E _{1}/E _{0}=1/2$. 


After second collision, $E _{2}/E _{0}=(1/2)^{2}$, therefore after $n$ collision.
           $\dfrac{E _{n}}{E _{0}}=(\dfrac{1}{2})^{n}$ 


Here, given $E _{0}=2MeV , E _{n}=0.04eV=0.04\times10^{-6}MeV$ 

Hence, $\dfrac{0.04\times10^{-6}}{2}=(\dfrac{1}{2})^{n}$ 

             $2\times10^{-8}=(\dfrac{1}{2})^{n}$ 

             $log 2-8log10=-nlog2$ 

             $0.3010-8=-0.3010n$ 

             $n=0.7699/0.3010=25.58$

Multiple choice nuclear reactions nuclear structure nuclei atomic nuclei physics

Find the energy released during the following nuclear reaction.


$ _{1}{H}^{1}  +   _{3}{Li}^{7}  \longrightarrow   _{2}{He}^{4}  +   _{2}{He}^{4}$

The mass of $ _{3}{Li}^{7}$ is $7.0160  u$,  $ _{2}{He}^{4}$ is $4.0026  u$ and proton is $1.0078  u$.

  1. 19.285  MeV

  2. <span>14.232 MeV</span>

  3. <span>17.326 MeV</span>

  4. <span>23.564 MeV</span>
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The mass of the reactant nuclei $= 7.0160 + 1.0078 = 8.0238  u$
The mass of the product nuclei $= 4.0026 + 4.0026 = 8.0052  u$
Mass defect $= \Delta m = 8.0238 - 8.0052 = 0.0186  u$
Energy released $= 0.0186  u \times 931.5  MeV = 17.326  MeV$

Multiple choice nuclear reactions nuclear structure nuclei atomic nuclei physics

The binding energy of $ _{3}{Li}^{7}$ and $ _{2}{He}^{4}$ are $39.2  MeV$ and $28.24  MeV$ respectively. Which of the following statements is correct?

  1. Helium is more stable than lithium.

  2. <span>Lithium is more stable than helium.</span>

  3. <span>Both are equally stable</span>

  4. <span>None of the above</span>
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The nucleons present in $ _{3}{Li}^{7}$ is $7$.
The binding energy per nucleon for lithium is ${39.2}/{7} = 5.6  MeV$
The binding per nucleon for helium is ${28.24}/{4} = 7.06  MeV$
The binding energy per nucleon is the measure of stability of the nuclei. Therefore, helium is more stable than lithium.

Multiple choice nuclear reactions nuclear structure nuclei atomic nuclei physics

Katen was studying nuclear physics. There, he collected values of binding energies of $ _{1}{H}^{2},   _{2}{He}^{4},   _{26}{Fe}^{56}$ and $ _{92}{U}^{235}$ and they are $2.22  MeV,  28.3  MeV,  492  MeV$ and $1786  MeV$ respectively. Then, he got a doubt that stability of the nucleus depends on its binding energy, which among the above four is the most stable nucleus?

  1. ${He} _{2}^{4}$

  2. ${U} _{92}^{235}$

  3. $ _{1}{H}^{2}$

  4. $ _{26}{Fe}^{56}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
Stability of nucleus $\alpha$ $\cfrac{Binding\;Energy}{Atomic\;mass}$
So, ${ _{ 1 }{ H }^{ 2 } }\rightarrow \cfrac { 2.22 }{ 2 } =1.11,\quad { _{ 2 }{ He }^{ 4 } }\rightarrow \cfrac { 28.3 }{ 4 } =7.075\\ { _{ 26 }{ Fe }^{ 56 } }\rightarrow \cfrac { 492 }{ 56 } =8.7,\quad { _{ 92 }{ U }^{ 235 } }\rightarrow \cfrac { 1786 }{ 235 } =7.6$
So, ${ _{ 26 }{ Fe }^{ 56 } }$ is stable among all four.
Multiple choice nuclear reactions nuclear structure nuclei atomic nuclei physics

In the nuclear reaction, there is a conservation of ______.

  1. momentum

  2. mass

  3. energy

  4. all of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

In a nuclear reaction, there may be conversion of some mass into energy. So,both mass and energy are not conserved. It is the momentum which is conserved.a

Multiple choice nuclear reactions nuclear structure nuclei atomic nuclei physics

The difference between a nuclear reactor and an atomic bomb is that

  1. no chain reaction takes place in nuclear reactor while in the atomic bomb there is a chain reaction

  2. the chain reaction in nuclear reactor is controlled

  3. the chain reaction in nuclear reactor is not controlled

  4. no-chain reaction takes place in atomic bomb while it takes place in nuclear reactor
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The chain reaction in nuclear reactor is controlled 

Both in nuclear reactor and atomic bomb nuclear fission takes place. But in nuclear reactor controlled fission chain reaction takes place while in atomic bomb chain reaction is uncontrolled. 

Multiple choice nuclear reactions nuclear structure nuclei atomic nuclei physics

The energy equivalent of $1\ amu$ is

  1. $931\ eV$

  2. $93.1\ V$

  3. $931\ MeV$

  4. $9.31\ MeV$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$1\ amu =1.66\times 10^{-27} kg$


According to Einstein's mass energy equivalence, $E=mc^2$ where $c=$ velocity of light. 

So, $E=1.66\times 10^{-27}\times (3\times 10^8)^2=14.94\times 10^{-11} J$

$E=\dfrac{14.94\times 10^{-11}}{1.6\times 10^{-19}} eV$       where $1eV=1.6\times 10^{-19} J$

$E=931\times 10^{6} eV=931\ MeV$

Multiple choice nuclear reactions nuclear structure nuclei atomic nuclei physics

The binding energy per nucleon of $^{16}O$ is $7.97MeV$ and that of $^{17}O$ is $7.75MeV$. The energy in MeV required to remove a neutron from $^{17}O$ is:

  1. $3.52$

  2. $3.64$

  3. $4.23$

  4. $7.86$

  5. $1.68$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

BE per nucleon $^{16}O=7.97MeV$
BE per nucleon $^{17}O=7.75MeV$
$^{17}O\rightarrow { _0n^1}+{^{16}O}$
Energy required to remove neutron
$=17\times 7.75-16\times 7.97$
$=4.23MeV$.