Chapter 11: Q23E (page 518)

Calculate the binding energy per nucleon of carbon- $12$ .

Short Answer

Expert verified

Binding energy per nucleons is $7.68 \frac{MeV}{nucleons}$ .

Step by step solution

Given data

Total number of nucleons, $A = 12$ .

Carbon $- 12$ has $Z$ (proton $) = 6$ and $N ($ neutron $) = = A - Z = 12 - 6 = 6$ .

Atomic number of hydrogen, $m_{H} = 1.007825 u$ .

Mass of neutron, $m_{n} = 1.008665 u$ .

Speed of light, $c = 3 \times 10^{8} m / s$ .

Atomic mass of technetium, $M_{\frac{12}{6} C} = 12 u$ .

Formula for Binding energy

For helium- $4$ , binding energy is given by formula, $B E = (Z m_{H} + N m_{n} - M_{\frac{4}{1} x}) c^{2}$ .

Calculation for the binding energy per nucleons

The binding energy per nucleons is given as:

$\begin{array}{l} \frac{BE}{nucleons} = \frac{{({Zm}_{H} {+Nm}_{n} {-M}_{\frac{12}{6}} c)}^{c^{2}}}{A} \\ \frac{BE}{nucleons} = \frac{[6 (1.007825 u) + 6 (1.008665 u) - 12 u] c^{2}}{12} \end{array}$

The conversion factor may be used to express $c^{2}$ in $MeV / u$ .

$\begin{array}{l} \frac{BE}{nucleons} = \frac{[6 (1.007825 u) + 6 (1.008665 u) - 12 u] (931.5 \frac{MeV}{a})}{12 nucleons} \\ \frac{BE}{nucleons} = 7.68 \frac{MeV}{nucleons} \end{array}$

Therefore, binding energy per nucleons is $7.68 \frac{MeV}{nucleons}$ .

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Calculate the binding energy per nucleon of carbon- $12$ .

Short Answer

Step by step solution

Given data

Formula for Binding energy

Calculation for the binding energy per nucleons

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Calculate the binding energy per nucleon of carbon- 12.

Short Answer

Step by step solution

Given data

Formula for Binding energy

Calculation for the binding energy per nucleons

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Conservation of Energy and Momentum

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Study anywhere. Anytime. Across all devices.

Calculate the binding energy per nucleon of carbon- $12$ .