Question

52. Binding energy per nucleon vs mass number cure for nuclei is shown in the figure. W, X, Y and Z are four nuclei indicated on the curve. The process that would release energy is:

• A. Y $\rightarrow$ 2Z
• B. W $\rightarrow$ X+Z
• C. W $\rightarrow$ 2Y
• D. X $\rightarrow$ Y+Z

Answer 1

Answer: (C)

C

Answer 2

Energy is released in a nuclear reaction if the total binding energy of the products is greater than the total binding energy of the reactants. The total binding energy of a nucleus is given by the product of its mass number ($A$) and the binding energy per nucleon ($E_b$).

From the graph for question 52:

• Nucleus Y: Mass number $\approx 60$, Binding energy per nucleon ($E_{bY}$) $\approx 8.5$ MeV.
• Nucleus X: Mass number $\approx 90$, Binding energy per nucleon ($E_{bX}$) $\approx 8.0$ MeV.
• Nucleus W: Mass number $\approx 120$, Binding energy per nucleon ($E_{bW}$) $\approx 7.5$ MeV.
• Nucleus Z: Mass number $\approx 30$, Binding energy per nucleon ($E_{bZ}$) $\approx 5.0$ MeV.

Let's analyze each option: (A) $Y \rightarrow 2Z$: Mass number conservation: $60 \rightarrow 2 \times 30 = 60$. Total binding energy of Y = $60 \times E_{bY} \approx 60 \times 8.5 = 510$ MeV. Total binding energy of 2Z = $2 \times (30 \times E_{bZ}) \approx 2 \times (30 \times 5.0) = 300$ MeV. Energy released = $B.E._{products} - B.E._{reactants} = 300 - 510 = -210$ MeV. (Energy absorbed)

(B) $W \rightarrow X+Z$: Mass number conservation: $120 \rightarrow 90 + 30 = 120$. Total binding energy of W = $120 \times E_{bW} \approx 120 \times 7.5 = 900$ MeV. Total binding energy of X+Z = $(90 \times E_{bX}) + (30 \times E_{bZ}) \approx (90 \times 8.0) + (30 \times 5.0) = 720 + 150 = 870$ MeV. Energy released = $870 - 900 = -30$ MeV. (Energy absorbed)

(C) $W \rightarrow 2Y$: Mass number conservation: $120 \rightarrow 2 \times 60 = 120$. Total binding energy of W = $120 \times E_{bW} \approx 120 \times 7.5 = 900$ MeV. Total binding energy of 2Y = $2 \times (60 \times E_{bY}) \approx 2 \times (60 \times 8.5) = 2 \times 510 = 1020$ MeV. Energy released = $1020 - 900 = 120$ MeV. (Energy released)

(D) $X \rightarrow Y+Z$: Mass number conservation: $90 \rightarrow 60 + 30 = 90$. Total binding energy of X = $90 \times E_{bX} \approx 90 \times 8.0 = 720$ MeV. Total binding energy of Y+Z = $(60 \times E_{bY}) + (30 \times E_{bZ}) \approx (60 \times 8.5) + (30 \times 5.0) = 510 + 150 = 660$ MeV. Energy released = $660 - 720 = -60$ MeV. (Energy absorbed)

The process that releases energy is $W \rightarrow 2Y$. This is a fission process where a heavier nucleus (W) splits into lighter nuclei (Y), and the products (Y) are more tightly bound (higher binding energy per nucleon) than the reactant (W).