Tag: nuclear reactions

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Questions Related to nuclear reactions

Multiple choice nuclear reactions nuclear structure nuclei atomic nuclei physics

The binding energy per nucleon of deutron $(^2 _1 H)$ and helium nucleus $(^4 _2 He)$ is 1.1 MeV and 7 MeV respectively. If two deutron nuclei react to form a single helium nucleus, then the energy released is

  1. $23.6 MeV$
  2. $26.9 MeV$
  3. $13.9 MeV$
  4. $19.2 MeV$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Energy released = BE(He) - 2 * BE(deuteron) = (4 * 7) - 2 * (2 * 1.1) = 28 - 4.4 = 23.6 MeV.

Multiple choice nuclear reactions nuclear structure nuclei atomic nuclei physics

Binding energy per nucleon is $8.5 \text { MeV for } A = 120$ and is $7.6 \mathrm { MeV } \text { for } \mathrm { A } = 240$ Suppose a nucleus with $A = 240$ breaks into two nuclei of nearly equal mass numbers then which of the following is correct

  1. 216 MeV energy is released.

  2. 21 MeV energy is to be given from outside

  3. 220 MeV energy is released.

  4. no energy is released.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Initial BE = 240 * 7.6 = 1824 MeV. Final BE = 2 * (120 * 8.5) = 2 * 1020 = 2040 MeV. Energy released = 2040 - 1824 = 216 MeV.

Multiple choice nuclear reactions nuclear structure nuclei atomic nuclei physics

Energy released if mass of $2\ amu$ is converted into energy is :

  1. $1.5 \times 10^{-10}\ J$
  2. $3 \times 10^{-10}\ J$
  3. $1863\ J$
  4. $931.5 \Mev$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$ E = \Delta m c^{2}$
    $ = (2 \times 1.67 \times 10^{-27}  kg) \times (3 \times 10^{8} \frac{m}{s})^{2} $
    $ = 3 \times 10^{-10}  J$

Multiple choice nuclear reactions nuclear structure nuclei atomic nuclei physics

When an electron and a positron are annihilated, then the number of photons produced is

  1. 2

  2. 1

  3. 3

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

Two photons are produced during the annihilation of an electron and a positron along with $1.02$ MeV released energy.

Multiple choice nuclear reactions nuclear structure nuclei atomic nuclei physics

Consider the nuclear reaction: $\mathrm { X } ^ { 200 } \longrightarrow \mathrm { A } ^ { 110 } + \mathrm { B } ^ { 20 }$If the binding energy per nucleon for $\mathrm { X } , \mathrm { A }$ and $\mathrm { B }$ is $7.4 \mathrm { MeV } , 8.2 \mathrm { MeV }$ and 8.2$\mathrm { MeV }$ respectively, what is the energy relesed?

  1. $200$ $\mathrm { MeV }$
  2. $160$ $\mathrm { MeV }$
  3. $110$ $\mathrm { MeV }$
  4. $90$ $\mathrm { MeV }$
Reveal answer Fill a bubble to check yourself
B Correct answer
Multiple choice nuclear reactions nuclear structure nuclei atomic nuclei physics

In the nucleus of helium if ${ F } _{ 1 }$ is the net force between two protons ${ F } _{ 2}$ is the net force between two neutrons and ${ F } _{ 3 }$ is the net force between a proton and a neutron. Then,

  1. ${ F } _{ 1 }={ F } _{ 2 }={ F } _{ 3 }$
  2. ${ F }> _{ 1 }{ F } _{ 2 }{ >F } _{ 3 }$
  3. ${ F }> _{ 2 }{ F } _{ 3 }{ >F } _{ 1 }$
  4. ${ F } _{3}={ F } _{ 1 }{ >F } _{ 2 }$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Nuclear forces are the strong forces of attraction which hold together the nucleons (neutrons and protons) in the tiny nucleus of an atom, inspite of strong electrostatic forces of repulsion between protons. Nuclear forces act between a pair of neutrons, a pair of protons and also between a neutron, proton pair with the same strength. This shows that nuclear forces are independent of charge. 
The attractive nuclear force is the same for any pair of nucleons. Thus$ F _1 = F _3$ when there are no electrostatic forces, but $F _2 =$ attractive nuclear force - repulsive electrostatic force
Hence
$F _3 = F _1 > F _2$
Multiple choice nuclear reactions nuclear structure nuclei atomic nuclei physics

The binding energy of $\alpha $-particle is ( if ${ m } _{ p }=1000785$ $u,{ m } _{ n }=1.00866$ u and ${ m } _{ \alpha  }=4.00274u$)

  1. $56.42 MeV$
  2. $2.821 MeV$
  3. $28.21 MeV$
  4. $32.4 MeV$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Mass defect: Δm = (2mp + 2mn) - mα = 2(1.00785) + 2(1.00866) - 4.00274 = 0.03028 u. BE = Δm × 931.5 MeV/u = 0.03028 × 931.5 ≈ 28.21 MeV. Note: Problem shows mp = 1000785 u which appears to be a typo for 1.00785 u.

Multiple choice nuclear reactions nuclear structure nuclei atomic nuclei physics

For a pair production, the minimum frequency of the gamma ray must be:

  1. 2.5 x 10$^{14}$ Hz
  2. 2.5 x 10$^{20}$ Hz
  3. 2.5 x 10$^{28}$ Hz
  4. 2.5 x 10$^{34}$ Hz
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For production to occur, the energy must be greater than the rest mass of proton + electron.
$E > ( 2 \times 0.511\ MeV = 1.022\ MeV)$
$h \nu > 1.022 \times  10^{6} \times 1.6 \times 10^{-19} J$
$\nu > \dfrac{1.6352 \times  10^{-13}}{h} = 2.5 \times 10^{20} Hz$

Multiple choice nuclear reactions nuclear structure nuclei atomic nuclei physics

The energy released when a positron is annihilated is

  1. $0.51 MeV$
  2. $0.58 MeV$
  3. $185 MeV$
  4. $200 MeV$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Positron, also called positive electron,  positively charged subatomic particle having the same mass and magnitude of charge as the electron.

mass of $e^+ = 9.11\times 10^{-31}Kg$

$E =mc^2=  9.11\times 10^{-31}\times (3\times 10^8)^2  J$

                 $= {0.51  \ MeV}$

The energy of annihilation of positron is ${0.51 \ MeV}$.
Multiple choice nuclear reactions nuclear structure nuclei atomic nuclei physics

If the energy of an electron in Hydrogen atom is given by expression, $-1312 /{ n }^{ 2 }kJ{ mol }^{ -1 }$, then the energy required to excite the electron from ground state to second orbit is 

  1. $328 kJ{ mol }^{ -1 }$
  2. $656 kJ{ mol }^{ -1 }$
  3. $984 kJ{ mol }^{ -1 }$
  4. $1312 kJ{ mol }^{ -1 }$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$\begin{array}{l} E=-1312\left( { \frac { 1 }{ 4 } -1 } \right)  \ =\frac { { -1312\times 3 } }{ 4 }  \ =328\times 3 \ =984\, kJmo{ l^{ -1 } } \ Hence, \ option\, \, C\, \, is\, \, correct\, answer. \end{array}$