Tag: nuclei

Questions Related to nuclei

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 $1.66\times { 10 }^{ -27 }㎏$

If mass-energy equvalence is taken into account, when water is cooled to form ice, the mass of ater should

nuclear reactions nuclear structure nuclei atomic nuclei physics

  1. Increase

  2. Remain unchanged

  3. decrease

  4. First increase and then decrease

Show answer
Correct Option: C
Explanation:

As we know that when water is converted into ice then it releases 

energy to the atmosphere, in other words, it can be said that
 it releases some mass to the atmosphere because mass and 
energy are equivalent. 
So option C is correct that mass will decrease.

Two light nuclei of masses $m _1$ and $m _2 $ are fused to form a more stable nucleus of mass $m _3$ then :-

nuclear reactions nuclear structure nuclei atomic nuclei physics

  1. $m _3 = | m _1 - m _2 | $

  2. $m _3 < ( m _1 + m _2 ) $

  3. $m _3 > ( m _1 - m _2 ) $

  4. $m _3 = | m _1 + m _2 | $

Show answer
Correct Option: B
Explanation:

When two nuclei of masses ${m _1}$ and ${m _2}$ are fused to form a stable nucleus of mass ${m _3}$ and some of the mass is converted in energy.

Therefore,

${m _3} < {m _1} + {m _2}$

A photon of $1.7 \times 10 ^{-13}$ joule is absorbed by a material under special circumstances. The correct statement is :

nuclear reactions nuclear structure nuclei atomic nuclei physics

  1. Electron of the atoms of absorbed material will go the higher energy states.

  2. Electron and positron pair will be created

  3. Only positron pair will be produced

  4. Photoelectric effect will occur and electron will be produced

Show answer
Correct Option: B
Explanation:

For electron and positron pair production, minimum energy is $1.02\ MeV$.
Energy of photon is given: $ 1.7 \times 10^{-3} J=\dfrac{1.7 \times 10^{-13}}{1.6 \times 10^{-19}}$$=1.06 \, MeV$.
Since energy of photon is greater than 1.02 MeV, electron positron pair will be created.