Paragraph: The mass of a nucleus _ Z ^ A X is less than the sum of...

Paragraph: The mass of a nucleus

{ }_{Z}^{A} X

is less than the sum of the masses of

(A-Z)

number of neutrons and

Z

number of protons in the nucleus. The energy equivalent to the corresponding mass difference is known as the binding energy of the nucleus. A heavy nucleus of mass

M

can break into two light nuclei of masses

m_{1} and m_{2}

only if

\left(m_{1}+m_{2}\right) \lt M

. Also two light nuclei of masses

m_{3} and m_{4}

can undergo complete fusion and form a heavy nucleus of mass

M^{\prime}

only if

\left(m_{3}+m_{4}\right) \gt M^{\prime}

. The masses of some neutral atoms are given in the table below: Paragraph: The mass of a nucleus _ Z ^ A X is less than the sum of the masses of (A-Z) number of neutrons and Z number

Paragraph: The mass of a nucleus _ Z ^ A X is less than the sum of the masses of (A-Z) number of neutrons and Z number

\left(1 u=932 M e V / c^{2}\right)

Question: The correct statement is

Options

AThe nucelus ${}_{\text{3}}^{\text{6}} \text{Li}$ can emit an alpha particle.
BThe nucleus ${}_{\text{84}}^{\text{210}} \text{Po}$ can emit a proton.
CDeuteron and alpha particle can undergo complete fusion.
DThe nuclei ${}_{\text{30}}^{\text{70}} \text{Zn}$ and ${}_{\text{34}}^{\text{82}} \text{Se}$ can undergo complete fusion.

Correct answer

C. Deuteron and alpha particle can undergo complete fusion.

Step-by-step solution

\text{(A)} {}_{3} {Li}^{7} \to {{}_{2} \text{He}}^{4} + {{}_{1} \text{H}}^{3}

\Delta \text{m} = \left[{\text{M}}_{\text{Li}} - {\text{M}}_{\text{He}} - \text{M} {\text{H}}^{3}\right]

= \left[\text{6.01513} - \text{4.002603} - \text{3.016050}\right]

= - \text{1.003523 u}

\Delta \text{m}

is negative so reaction n is not possible.

\text{(B)} {}_{84} {Po}^{210} \to {{}_{83} \text{Bi}}^{209} + {{}_{1} \text{P}}^{1}

\Delta \text{m}

is negative so reaction is not possible.

\text{(C)} {}_{1} {H}^{2} \to {{}_{2} \text{He}}^{4} + {{}_{3} \text{Li}}^{6}

\Delta \text{m}

is positive so reaction is possible.

\text{(D)} {}_{30} {Zn}^{70} + {{}_{34} \text{Se}}^{82} \to {{}_{64} \text{Gd}}^{152}

\Delta \text{m}

is positive so reaction is not possible.

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