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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

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

Multiple choice nuclear reactions nuclear structure nuclei atomic nuclei physics

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

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

  1. a,b

  2. c,d

  3. b,c,d

  4. only d
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

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

Multiple choice nuclear reactions nuclear structure nuclei atomic nuclei physics

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.

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

Multiple choice nuclear reactions nuclear structure nuclei atomic nuclei physics

Choose the correct statement :

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