Tag: nuclear structure

Questions Related to nuclear structure

Which of the following relations is correct?

nuclear reactions nuclear structure nuclei atomic nuclei physics

  1. $E = mc$

  2. $E = mc^2$

  3. $E = 2mc^2$

  4. $E = mc^2/4$

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Correct Option: B
Explanation:

According to Einstein, energy and mass are related by the relation.
$E = mc^2$
where c is the speed of light in vacuum.

One milligram of matter is converted into energy. The energy released will be

nuclear reactions nuclear structure nuclei atomic nuclei physics

  1. $9\times 10^{6} J$

  2. $9\times 10^{8}J$

  3. $9\times 10^{10}J$

  4. $9\times 10^{12}J$

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Correct Option: C
Explanation:

Here, $m = 1\ mg = 1\times 10^{-3} g $

             $= 1\times 10^{-6}kg$
According to Einstein mass-energy equivalence
                $E = mc^{2}$
where $c$ is the speed of light in vacuum
$\therefore E = (1\times 10^{-6} kg)(3\times 10^{8}ms^{-1})^{2}$
$ = 9\times 10^{10}J$.

The relation between the volume $V$ and the mass $M$ of a nucleus is:

nuclear reactions nuclear structure nuclei atomic nuclei physics

  1. $V\propto M^{3}$

  2. $V\propto M^{1/3}$

  3. $V\propto M$

  4. $V\propto 1/M$

Show answer
Correct Option: C
Explanation:

Since the density of nucleus is fixed.

$D=\cfrac { M }{ V } \ \Rightarrow M=DV\ M\propto V$

A student wrote the relation for one unified atomic mass unit (u) as $1u=931.5MeV$. What is the correct relation?

nuclear reactions nuclear structure nuclei atomic nuclei physics

  1. $1 u\times c=931.5 MeV$

  2. $1 u\times c^2=931.5 MeV$

  3. $\dfrac{1u}{c^2}=931.5 MeV$

  4. $(1u)^2\times c=931.5Me V$

Show answer
Correct Option: B
Explanation:

$1u=931.5 MeV$
we know $1u=1.66\times 10^{-21}kv$
$931.5 MeV=931.5\times 10^6\times 1.6\times 10^{-19}J=1.49\times 10^{-10}$
$E=(1u)(c^2)=(1.66\times 10^{-27})(3\times 10^8)^2J=1.494\times 10^{-10}J$
so $(1u)(c)^2=931.5MeV$

A nucleus of mass number $A$ originally at rest emits $\alpha$- particle with speed $v$. The recoil speed of daughter nucleus is:

nuclear reactions nuclear structure nuclei atomic nuclei physics

  1. $\cfrac{4v}{A-4}$

  2. $\cfrac{4v}{A+4}$

  3. $\cfrac{v}{A-4}$

  4. $\cfrac{v}{A+4}$

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Correct Option: A

As the mass number increase, binding energy per nucleon,

nuclear reactions nuclear structure nuclei atomic nuclei physics

  1. increases

  2. decreases

  3. remain same

  4. may increase or may decrease

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Correct Option: D

Per nucleon energy of $ _ { 3 } L ^ { 7 }$ and $2 ^ { \mathrm { H } e ^ { 4 } }$  nucleus is 5. 60  MeV and 7.06 MeV then in$ _ { 3 } \mathrm { L } ^ { 7 } + _ { 1 } \mathrm { P } ^ { 1 } \rightarrow 2 _ { 2 } \mathrm { He } ^ { 4 }$ energy released is:

nuclear reactions nuclear structure nuclei atomic nuclei physics

  1. $29.6 \mathrm { MeV }$

  2. $2.4MeV$

  3. $8.4 \mathrm { MeV }$

  4. $17.3 \mathrm { MeV }$

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Correct Option: A

Mass defect of an atom refers to 

nuclear reactions nuclear structure nuclei atomic nuclei physics

  1. inaccurate measurement of mass of neutrons

  2. mass annihilated to produce energy to bind the nucleons

  3. packing fraction

  4. difference in the number of neutrons and protons in the nucleus

Show answer
Correct Option: B
Explanation:

$ Mc^{2} + (B.E) = (N _{mN} + Z _{mP})c^{2}$
where,
         $M _{c} =  $  total mass of nucleus.
         $N _{mN} =  $  total mass of neutrons
         $N _{mP}  =  $  total mass of protons

In a fission process, nucleus A divides into two nuclei B and C, their binding energies being $\mathbf { E } _ { \mathbf { a } ^ { * } }$   $E _ { b }$  and $E _ { c }$ respectively. Ihen

nuclear reactions nuclear structure nuclei atomic nuclei physics

  1. $\mathbf { E } _ { \mathrm { b } } + \mathrm { E } _ { \mathrm { c } } = \mathrm { E } _ { \mathrm { a } }$

  2. $\mathrm { E } _ { \mathrm { b } } + \mathrm { E } _ { \mathrm { c } } > \mathrm { E } _ { \mathrm { a } }$

  3. $\mathrm { E } _ { \mathrm { b } } + \mathrm { E } _ { \mathrm { e } } < \mathrm { E } _ { \mathrm { a } }$

  4. $\mathrm { E } _ { \mathrm { b } } \mathrm { E } _ { \mathrm { c } } = \mathrm { E } _ { \mathrm { a } }$

Show answer
Correct Option: A
Explanation:

$\begin{array}{l} { E _{ b } }+{ E _{ c } }>{ E _{ a } } \ \, \because some\, \, energy\, \, is\, \, goen\, \, in\, \, breaking\, \, nuclie\, \, of\, \, A \ Hence, \ option\, \, A\, \, is\, \, correct\, \, answer. \end{array}$

For uranium nucleus. Find relation between mass and volume 

nuclear reactions nuclear structure nuclei atomic nuclei physics

  1. $m\propto v$

  2. $m\propto \sqrt{v}$

  3. $m\propto v^2$

  4. $m\propto \dfrac{1}{v}$

Show answer
Correct Option: A