Tag: nuclei

Questions Related to nuclei

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

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Correct Option: A

The phenomenon of pair production is :

nuclear reactions nuclear structure nuclei atomic nuclei physics

  1. The production of an electron and a positron from $\gamma$ radiation

  2. Ejection of an electron from a metal surface when exposed to ultraviolet light

  3. Ejection of an electron from a nucleus

  4. Ionization of a neutral atom

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Correct Option: A
Explanation:

Pair production :
Gamma rays of sufficient energy when passing near a nucleus disappear and materialize into pair of an electron and a positron.
To have pair production, minimum energy of $\gamma$ - ray radiation is 1.02MeV.

In pair annihilation the least number of  $\gamma $- ray photons produced is :

nuclear reactions nuclear structure nuclei atomic nuclei physics

  1. 2

  2. 3

  3. 4

  4. 1

Show answer
Correct Option: A
Explanation:

In a pair annihilation, atleast two gamma rays must be produced. For example, when an electron encounters a positron, they annihilate to produce two gamma rays each having $0.511$ MeV energy.

The rest energy of electron or positron is

nuclear reactions nuclear structure nuclei atomic nuclei physics

  1. 0.51 MeV

  2. 1 MeV

  3. 1.02 MeV

  4. 1.5 MeV

Show answer
Correct Option: A
Explanation:

Mass of electron $ = 9.1 \times 10^{-31}  kg$

Rest mass energy $ = mc^{2}$


                               $ =\left (\dfrac{9.1\times 10^{-31}}{1.6\times10^{-27}} \times931.978\right )c^{2}$

                               $ = 0.52\  MeV$