Tag: nuclear reactions

Questions Related to nuclear reactions

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?

nuclear reactions nuclear structure nuclei atomic nuclei physics

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

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

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

  4. $ _{26}{Fe}^{56}$

Show answer
Correct Option: D
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.

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

nuclear reactions nuclear structure nuclei atomic nuclei physics

  1. momentum

  2. mass

  3. energy

  4. all of these

Show answer
Correct Option: A
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

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

nuclear reactions nuclear structure nuclei atomic nuclei physics

  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

Show answer
Correct Option: B
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. 

The energy equivalent of $1\ amu$ is

nuclear reactions nuclear structure nuclei atomic nuclei physics

  1. $931\ eV$

  2. $93.1\ V$

  3. $931\ MeV$

  4. $9.31\ MeV$

Show answer
Correct Option: C
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 $1eV=1.6\times 10^{-19} J$

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

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:

nuclear reactions nuclear structure nuclei atomic nuclei physics

  1. $3.52$

  2. $3.64$

  3. $4.23$

  4. $7.86$

  5. $1.68$

Show answer
Correct Option: C
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
$=17\times 7.75-16\times 7.97$
$=4.23MeV$.

The mass defect of a certain nucleus is found to be $0.03$ amu. Its binding energy is:

nuclear reactions nuclear structure nuclei atomic nuclei physics

  1. $27.93$ eV

  2. $27.93$ keV

  3. $27.93$ MeV

  4. $27.93$ GeV

Show answer
Correct Option: A
Explanation:

Mass defect  $\Delta M = 0.03$ amu
Binding energy  $E _{B} = \Delta Mc^2 = \Delta M\times 931.5 $  MeV
$\therefore \ E _{B} = 0.03\times 931.5$ MeV $ =27.93 $ MeV

Consider the following statements
(i)All isotopes of an element have the same number of neutrons
(ii)Only one isotope of an element can be stable and non -radioactive
(iii)All elements have isotopes  
(iv)All isotopes of Carbon can form chemical compounds with Oxygen -16
The correct option regarding an isotope is 

nuclear reactions nuclear structure nuclei atomic nuclei physics

  1. (iii) and (iv) only

  2. (ii),(iii) and (iii) only

  3. (i),(ii) and (iii) only

  4. (i),(iii) and (iv) only

Show answer
Correct Option: A
Explanation:

A

Isotopes are atoms of the same element having the same numbers of protons and different numbers of neutrons. All elements have isotope. Also all isotope of carbon can form chemical compounds with oxygen - 16.

Higher the mass defect, higher will be the stability of the nucleus.

nuclear reactions nuclear structure nuclei atomic nuclei physics

  1. True

  2. False

Show answer
Correct Option: B
Explanation:
Amount of energy required to break the nucleus is known as binding energy of the nucleus.
It depends upon mass defect.
Greater  the mass defect, greater will be the binding energy
Stable nuclei have high binding energies

1 u is equivalent to an energy of

nuclear reactions nuclear structure nuclei atomic nuclei physics

  1. 9.315 MeV

  2. 931.5 KeV

  3. 93.15 MeV

  4. 931.5 MeV

Show answer
Correct Option: D
Explanation:
According to Einstein mass energy equivalence is represented by
$E=m{ c }^{ 2 }$
Taking $m=1a.m.u$
$=1.66\times { 10 }^{ -27 }㎏$
and $c=3\times { 10 }^{ 8 }㎧$
We get, $E=1.66\times { 10 }^{ -27 }\times { \left( 3\times { 10 }^{ 8 } \right)  }^{ 2 }J$
$=1.49\times { 10 }^{ -10 }J$
As $1MeV=1.6\times { 10 }^{ -13 }J$
$\therefore E=\cfrac { 1.49\times { 10 }^{ -10 } }{ 1.6\times { 10 }^{ -13 } } $
$E=931.25MeV$
Hence,$1a.m.u.=931.25MeV$

The mass equivalent of 931.5 MeV energy is

nuclear reactions nuclear structure nuclei atomic nuclei physics

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

  2. $6.02 \times 10^{-24}kg$

  3. $1.66 \times 10^{-20} kg$

  4. $6.02 \times 10^{-27} kg$

Show answer
Correct Option: A
Explanation:
According to Einstein, mass energy equivalence is represented by
$E=m{ C }^{ 2 }$
Taking $m=1a.m.u$
$=1.66\times { 10 }^{ -27 }㎏$
and $C=3\times { 10 }^{ 8 }㎧$
We get $E=1.66\times { 10 }^{ -27 }\times { (3\times { 10 }^{ 8 }) }^{ 2 }J$
$=1.49\times { 10 }^{ -10 }J$
As $1MeV=1.6\times { 10 }^{ -13 }J$
$\therefore E=\cfrac { 1.49\times { 10 }^{ -10 } }{ 1.6\times { 10 }^{ -13 } } $
$E=931.25MeV$
Hence the mass equivalent of $931.25MeV$ energy is $1.66\times { 10 }^{ -27 }㎏$