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Multiple choice nuclear reactions nuclear structure nuclei atomic nuclei physics

In which of the following nuclear reactions, the product is incorrectly matched ?

  1. $ _{96}Cm^{242}(\alpha, 2n) _{97}Bk^{243}$

  2. $ _5B^{10}(\alpha, n) _7N^{13}$

  3. $ _7N^{14}(n, p) _6C^{14}$

  4. $ _{14}Si^{28}(d, n) _{15}P^{29}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

In option A, the mass number change is 243-242 = 1, but the reaction is (alpha, 2n). An alpha particle adds 4 to the mass and 2 to the atomic number, while 2 neutrons remove 2 from the mass. The net change should be +2 mass and +2 atomic number, making the product Cm-242 + He-4 - 2n = Bk-244, not Bk-243.

Multiple choice nuclear reactions nuclear structure nuclei atomic nuclei physics

A proton and an alpha particle having same momentum enter a magnetic field at right angles to it. If $r _1$ and $r _2$ be their radii respectively then value of $r _1 /r _2$ is : 

  1. $1$

  2. $2$

  3. $1/2$

  4. $1/4$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The radius of a charged particle in a magnetic field is r = p / (qB). Since both particles have the same momentum p and enter the same field B, the ratio r1/r2 = q2/q1. A proton has charge 1 and an alpha particle has charge 2, so r1/r2 = 2/1 = 2.

Multiple choice nuclear reactions nuclear structure nuclei atomic nuclei physics

$A5\times 10^{-4}\overset {o}{A}$ photon produces an electron-positron pair in the vicinity of a heavy nucleus. Rest energy of electron is 0.5 11 MeV. If they have the same kinetic energies, the energy of each particle is nearly

  1. 1.2 MeV

  2. 12 MeV

  3. 120 MeV

  4. 1200 MeV
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Photon wavelength: λ = 5 × 10⁻⁴ Å = 5 × 10⁻¹⁴ m. Energy: E = hc/λ = (1240 eV·nm)/(5 × 10⁻⁵ nm) ≈ 24.8 MeV. Total rest energy of e⁻e⁺ pair: 2 × 0.511 = 1.022 MeV. Available kinetic energy: 24.8 - 1.022 ≈ 23.78 MeV. Each particle gets half: ≈ 11.89 MeV, approximately 12 MeV. Note: '0.5 11 MeV' appears to be typo for 0.511 MeV.

Multiple choice nuclear reactions nuclear structure nuclei atomic nuclei physics

If mass-energy equivalence is taken into account, when water is cooled to form ice, the mass of water should

  1. increase

  2. remain unchanged

  3. decrease

  4. first increase then decrease
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Because thermal energy decreases, therefore mass should increase.

Multiple choice nuclear reactions nuclear structure nuclei atomic nuclei physics

If 1mg of ${ U }^{ 235 }$ is completely annihilated, the energy liberated is

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

  2. $\quad 9\times { 10 }^{ 19} J$

  3. $\quad 9\times { 10 }^{ 18} J$

  4. $\quad 9\times { 10 }^{ 17} J$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$E={ mc }^{ 2 }={ 10 }^{ -6 }\times \left( 3\times { 10 }^{ 8 } \right) ^{ 2 }={ 10 }^{ -6 }\times 9\times { 10 }^{ 16 }=9\times { 10 }^{ 10 }J$

Multiple choice nuclear reactions nuclear structure nuclei atomic nuclei physics

One milligram of matter convert into energy will give

  1. $90 joule$

  2. $9\times { 10 }^{ 3} joule$

  3. $9\times { 10 }^{ 5} joule$

  4. $9\times { 10 }^{ 10} joule$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$E={ mc }^{ 2 }={ 10 }^{ -3 }\times{ 10 }^{ -3 } \left( 3\times { 10 }^{ 8 } \right) ^{ 2 }=9\times { 10 }^{ 10 }J$

Multiple choice nuclear reactions nuclear structure nuclei atomic nuclei physics

The mass and energy equivalent to $1 amu$ are respectively

  1. $1.67\times { 10 }^{ -27 }gm$, $9.30 MeV$

  2. $1.67\times { 10 }^{ -27 }kg$, $930 MeV$

  3. $1.67\times { 10 }^{ -27 }kg$,$ 1 MeV$

  4. $1.67\times { 10 }^{ -34 }kg$, $1 MeV$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

1 amu
It is defined as one twelfth of the mass of an unbound neutral atom of carbon-12 in its nuclear and electronic ground state.


Mass of 1 mole C atoms $= 12 gms$
$1\ amu = $$ \cfrac{12}{12 \times 6.023 \times 10^{23}} = 1.66 \times 10^{-27} kg$

Energy equivalent, $E = mc^2 =1.66 \times 10^{-27} kg \times (3 \times 10^8)^2$$ = 930\ MeV$

Multiple choice nuclear reactions nuclear structure nuclei atomic nuclei physics

If an electron and positron annihilate, then the energy released is

  1. $3.2\times { 10 }^{ -13 } J$

  2. $1.6\times { 10 }^{ -13 } J$

  3. $4.8\times { 10 }^{ -13 } J$

  4. $6.4\times { 10 }^{ -13 } J$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Energy of electron $={ m } _{ e }{ c }^{ 2 }$
Energy of positron $={ m } _{ p }{ c }^{ 2 }$
${ m } _{ e }$ = ${ m } _{ p }$, $ c=$ speed of light.

Thus according to conservation of energy released $=2{ m } _{ e }{ c }^{ 2 }$$=2\times 9.1\times { 10 }^{ -31 }\left( 3\times { 10 }^{ 8 } \right) ^{ 2 }=1.6\times { 10 }^{ -13 } Joules.$

Multiple choice nuclear reactions nuclear structure nuclei atomic nuclei physics

The rest energy of an electron is

  1. $510 KeV$

  2. $931 KeV$

  3. $510 MeV$

  4. $931 MeV$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Rest energy of an electron $=m _{ e }{ c }^{ 2 }$
Here $m _{ e }=9.1\times { 10 }^{ -31 }kg$ and $C$ = velocity of light

$\therefore$ Rest energy $=9.1\times { 10 }^{ -31 }\times\left( 3\times { 10 }^{ 8 } \right) ^{ 2 }joule$

                         $=\displaystyle \frac { 9.1\times { 10 }^{ -31 }\times \left( 3\times { 10 }^{ 8 } \right) ^{ 2 } }{ 1.6\times { 10 }^{ -19 } } eV\simeq 510KeV$

Multiple choice nuclear reactions nuclear structure nuclei atomic nuclei physics

1mg of matter convert into energy will give

  1. $90$ joule

  2. $9\times { 10 }^{ 3 }$ joule

  3. $9\times { 10 }^{ 5 }$ joule

  4. $9\times { 10 }^{ 10 }$ joule
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$E=m{ c }^{ 2 }=10^{ -3 }\times { 10 }^{ -3 }\times { \left( 3\times { 10 }^{ 8 } \right)  }^{ 2 }= 9\times { 10 }^{ 10 }J$