JEE Challenger
More from Nuclei
PhyMedAdv 2013 • Paper 2

Identification of Possible Nuclear Fusion and Fission Processes

Comprehension Passage

The mass of a nucleus ZAX_Z^A X is less than the combined mass of its (A−Z)(A-Z) constituent neutrons and ZZ protons. The energy equivalent of this mass difference represents the binding energy of the nucleus. A heavy nucleus with mass MM can disintegrate into two lighter nuclei of masses m1m_1 and m2m_2 provided that (m1+m2)<M(m_1+m_2) < M. Likewise, two light nuclei having masses m3m_3 and m4m_4 can undergo fusion to form a heavy nucleus of mass M′M' provided that (m3+m4)>M′(m_3+m_4) > M'. Atomic masses of certain neutral atoms are given in the following table:

11H1.007825 u12H2.014102 u13H3.016050 u24He4.002603 u36Li6.015123 u37Li7.016004 u3070Zn69.925325 u3482Se81.916709 u64152Gd151.919803 u82206Pb205.974455 u83209Bi208.980388 u84210Po209.982876 u\begin{array}{|c|c|c|c|c|c|c|c|} \hline _1^1 H & 1.007825\text{ u} & _1^2 H & 2.014102\text{ u} & _1^3 H & 3.016050\text{ u} & _2^4 He & 4.002603\text{ u} \\ \hline _3^6 Li & 6.015123\text{ u} & _3^7 Li & 7.016004\text{ u} & _{30}^{70} Zn & 69.925325\text{ u} & _{34}^{82} Se & 81.916709\text{ u} \\ \hline _{64}^{152} Gd & 151.919803\text{ u} & _{82}^{206} Pb & 205.974455\text{ u} & _{83}^{209} Bi & 208.980388\text{ u} & _{84}^{210} Po & 209.982876\text{ u} \\ \hline \end{array}

Use 1 u=932 MeV/c21\text{ u} = 932\text{ MeV}/c^2.

Which of the following options represents a correct statement regarding nuclear reactions?

Options

A

The nucleus 36Li_3^6 Li is capable of emitting an alpha particle.

B

The nucleus _{84}^{210} Po can spontaneously emit a proton.

C

A deuteron nucleus and an alpha particle can undergo complete fusion.

Correct
D

The two nuclei _{30}^{70} Zn and _{34}^{82} Se can undergo complete fusion.

Topics & Concepts

NucleiNuclear ReactionsRadioactivity

Step-by-Step Solution

To determine the correct statement, we analyze each option based on the conditions for nuclear fission (disintegration) and fusion given in the passage:

  1. Condition for Fission (Spontaneous Disintegration / Emission): A heavy nucleus MM can disintegrate into m1m_1 and m2m_2 if: m1+m2<Mm_1 + m_2 < M

  2. Condition for Fusion: Two light nuclei m3m_3 and m4m_4 can undergo fusion to form a heavy nucleus M′M' if: m3+m4>M′m_3 + m_4 > M'

Analysis of Options:

  • Option (A): Emissions of an α\alpha-particle by 36Li_3^6\text{Li} Reaction: 36Li⟶12H+24He\text{Reaction: } _3^6\text{Li} \longrightarrow _1^2\text{H} + _2^4\text{He}

    • Mass of initial nucleus, M=m(36Li)=6.015123 uM = m\left(_3^6\text{Li}\right) = 6.015123\text{ u}
    • Mass of products, m1+m2=m(12H)+m(24He)=2.014102 u+4.002603 u=6.016705 um_1 + m_2 = m\left(_1^2\text{H}\right) + m\left(_2^4\text{He}\right) = 2.014102\text{ u} + 4.002603\text{ u} = 6.016705\text{ u}

    Since m1+m2>Mm_1 + m_2 > M (6.016705 u>6.015123 u6.016705\text{ u} > 6.015123\text{ u}), spontaneous emission is not possible. Thus, Option (A) is incorrect.

  • Option (B): Spontaneous proton emission by 84210Po_{84}^{210}\text{Po} Reaction: 84210Po⟶83209Bi+11H\text{Reaction: } _{84}^{210}\text{Po} \longrightarrow _{83}^{209}\text{Bi} + _1^1\text{H}

    • Mass of initial nucleus, M=m(84210Po)=209.982876 uM = m\left(_{84}^{210}\text{Po}\right) = 209.982876\text{ u}
    • Mass of products, m1+m2=m(83209Bi)+m(11H)=208.980388 u+1.007825 u=209.988213 um_1 + m_2 = m\left(_{83}^{209}\text{Bi}\right) + m\left(_1^1\text{H}\right) = 208.980388\text{ u} + 1.007825\text{ u} = 209.988213\text{ u}

    Since m1+m2>Mm_1 + m_2 > M (209.988213 u>209.982876 u209.988213\text{ u} > 209.982876\text{ u}), proton emission is not possible. Thus, Option (B) is incorrect.

  • Option (C): Fusion of a deuteron (12H_{1}^{2}\text{H}) and an α\alpha-particle (24He_{2}^{4}\text{He}) Reaction: 12H+24He⟶36Li\text{Reaction: } _1^2\text{H} + _2^4\text{He} \longrightarrow _3^6\text{Li}

    • Mass of reactants, m3+m4=m(12H)+m(24He)=2.014102 u+4.002603 u=6.016705 um_3 + m_4 = m\left(_1^2\text{H}\right) + m\left(_2^4\text{He}\right) = 2.014102\text{ u} + 4.002603\text{ u} = 6.016705\text{ u}
    • Mass of fused nucleus, M′=m(36Li)=6.015123 uM' = m\left(_3^6\text{Li}\right) = 6.015123\text{ u}

    Since m3+m4>M′m_3 + m_4 > M' (6.016705 u>6.015123 u6.016705\text{ u} > 6.015123\text{ u}), complete fusion can take place. Thus, Option (C) is correct.

  • Option (D): Fusion of 3070Zn_{30}^{70}\text{Zn} and 3482Se_{34}^{82}\text{Se} Reaction: 3070Zn+3482Se⟶64152Gd\text{Reaction: } _{30}^{70}\text{Zn} + _{34}^{82}\text{Se} \longrightarrow _{64}^{152}\text{Gd}

    • Mass of reactants, m3+m4=m(3070Zn)+m(3482Se)=69.925325 u+81.916709 u=151.842034 um_3 + m_4 = m\left(_{30}^{70}\text{Zn}\right) + m\left(_{34}^{82}\text{Se}\right) = 69.925325\text{ u} + 81.916709\text{ u} = 151.842034\text{ u}
    • Mass of fused nucleus, M′=m(64152Gd)=151.919803 uM' = m\left(_{64}^{152}\text{Gd}\right) = 151.919803\text{ u}

    Since m3+m4<M′m_3 + m_4 < M' (151.842034 u<151.919803 u151.842034\text{ u} < 151.919803\text{ u}), complete fusion cannot occur. Thus, Option (D) is incorrect.

Conclusion: The correct statement is C.

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