Chapter 42: Q.42b. (page 1237)

Use the graph of binding energy to estimate the total energy released if three $^{4} He$ nuclei fuse together to form a $^{12} C$ nucleus.

Short Answer

Expert verified

The amount of energy released is $6.0 MeV$ .

Step by step solution

Step.1.

From the figure 42.6, plot binding energy per nucleon verse mass number given in the text book, the binding energy per nucleon for $^{4} He$ nucleus approximately is $7.2 MeV$ and the binding energy per nucleon for $^{12} C$ nucleus is $7.7 MeV$ .

The nucleus $^{4} He$ has 4 nucleons, so the total binding energy of one $^{4} He$ nucleus is,

$\begin{array}{l} {(Δ E)}_{^{4} He} = (4) (7.2 MeV) \\ = 28.8 MeV \end{array}$

The total binding energy of three $^{4} He$ nuclei is,

$\begin{array}{l} Δ E_{1} = (3) (28.8 MeV) \\ = 86.4 MeV \end{array}$

The nucleus $^{12} C$ has 12 nucleons, so the total binding energy of $^{12} C$ nucleus is,

$\begin{array}{l} Δ E_{2} = (12) (7.7 MeV) \\ = 92.4 MeV \end{array}$

Step.2.

The amount of energy released in the nuclear reaction which involves three $^{4} He$ nuclei fuse together and form a $^{12} C$ nucleus is,

$\begin{array}{l} Δ E = E_{2} - E_{1} \\ = 92.4 MeV - 86.4 MeV \\ = 6.0 MeV \end{array}$

Therefore, the amount of energy released is $6.0 MeV$ .

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Use the graph of binding energy to estimate the total energy released if three $^{4} He$ nuclei fuse together to form a $^{12} C$ nucleus.

Short Answer

Step by step solution

Step.1.

Step.2.

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Use the graph of binding energy to estimate the total energy released if three 4Henuclei fuse together to form a12C nucleus.

Short Answer

Step by step solution

Step.1.

Step.2.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Circular Motion and Gravitation

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Study anywhere. Anytime. Across all devices.

Use the graph of binding energy to estimate the total energy released if three $^{4} He$ nuclei fuse together to form a $^{12} C$ nucleus.