Tag: nuclei

Questions Related to nuclei

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

nuclear reactions nuclear structure nuclei atomic nuclei physics

  1. 2

  2. 1

  3. 3

  4. 4

Show answer
Correct Option: A
Explanation:

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

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?

nuclear reactions nuclear structure nuclei atomic nuclei physics

  1. $200$ $\mathrm { MeV }$

  2. $160$ $\mathrm { MeV }$

  3. $110$ $\mathrm { MeV }$

  4. $90$  $\mathrm { MeV }$

Show answer
Correct Option: B

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,

nuclear reactions nuclear structure nuclei atomic nuclei physics

  1. ${ F } _{ 1 }={ F } _{ 2 }={ F } _{ 3 }$

  2. ${ F }> _{ 1 }{ F } _{ 2 }{ >F } _{ 3 }$

  3. ${ F }> _{ 2 }{ F } _{ 3 }{ >F } _{ 1 }$

  4. ${ F } _{3}={ F } _{ 1 }{ >F } _{ 2 }$

Show answer
Correct Option: D
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
$F _3 = F _1 > F _2$

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

nuclear reactions nuclear structure nuclei atomic nuclei physics

  1. $56.42 MeV$

  2. $2.821 MeV$

  3. $28.21 MeV$

  4. $32.4 MeV$

Show answer
Correct Option: C

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

nuclear reactions nuclear structure nuclei atomic nuclei physics

  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

Show answer
Correct Option: B
Explanation:

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

The energy released when a positron is annihilated is

nuclear reactions nuclear structure nuclei atomic nuclei physics

  1. $0.51 MeV$

  2. $0.58 MeV$

  3. $185 MeV$

  4. $200 MeV$

Show answer
Correct Option: A
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 ${0.51 \ MeV}$.

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 

nuclear reactions nuclear structure nuclei atomic nuclei physics

  1. $328 kJ{ mol }^{ -1 }$

  2. $656 kJ{ mol }^{ -1 }$

  3. $984 kJ{ mol }^{ -1 }$

  4. $1312 kJ{ mol }^{ -1 }$

Show answer
Correct Option: C
Explanation:

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

$\gamma $ -ray photon of following energy undergoes pair production : 

a) $0.85Mev $      b) $1.00Mev $
c)  $1.02Mev $     d) $1.82Mev$

nuclear reactions nuclear structure nuclei atomic nuclei physics

  1. a,b

  2. c,d

  3. b,c,d

  4. only d

Show answer
Correct Option: B
Explanation:

The pair production becomes possible with gamma energies exceeding $1.02\ MeV$, and becomes important as an absorption mechanism at energies over $5\ MeV$.

Assertion (A) : Due to annihilation of electron positron pair, at least 2 $\gamma $-ray photons are produced.
Reason (R) : This is in accordance with conservation of linear momentum.

nuclear reactions nuclear structure nuclei atomic nuclei physics

  1. Both A & R are true and R is the correct explanation of A

  2. Both A & R are true and R is not correct explanation of A

  3. A is true but R is false

  4. A is false but R is true

Show answer
Correct Option: A
Explanation:

$ e^{-} + e^{+} \Rightarrow  \gamma +\gamma $
This annihilation is in accordance to three laws:-
1] conservation of linear momentum
2] conservation of charge
3] conservation of angular momentum
Two $\gamma $ ray photons are released on annihilation of electron and positron.

Choose the correct statement :

nuclear reactions nuclear structure nuclei atomic nuclei physics

  1. A nucleus is relatively more stable for which total binding energy is more.

  2. A nucleus is relatively more stable for which binding energy per nucleon is more.

  3. A nucleus is relatively more stable for which total binding energy is low.

  4. None of these

Show answer
Correct Option: A
Explanation:

Binding energy is the amount of energy required to separate a particle from a system of particles or to disperse all the particles of the system. Binding energy is especially applicable to subatomic particles in atomic nuclei, to electrons bound to nuclei in atoms, and to atoms and ions bound together in crystals. Binding energy is more if the nucleus is relatively more stable.