nuclear physics
mass defect and binding energy
5. if the mass of a li-6 nucleus is 6.01513 u, what is the mass defect and the binding energy of this nucleus?

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{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Mass Defect", "Nuclear Binding Energy" ], "new_concepts": [], "current_concepts": [ "Mass Defect", "Nuclear Binding Energy" ] } ## Identify the composition of Lithium-6 Using the *Mass Defect* knowledge point $$ \begin{aligned} &Z = 3 \quad (\text{protons})\ &N = 6 - 3 = 3 \quad (\text{neutrons})\ &m_p = 1.007276\text{ u}\ &m_n = 1.008665\text{ u}\ &m_{\text{nucleus}} = 6.01513\text{ u} \end{aligned} $$ ## Calculate the mass defect Using the *Mass Defect* knowledge point $$ \begin{aligned} \Delta m &= (Z \cdot m_p + N \cdot m_n) - m_{\text{nucleus}}\ \Delta m &= (3 \cdot 1.007276\text{ u} + 3 \cdot 1.008665\text{ u}) - 6.01513\text{ u}\ \Delta m &= (3.021828\text{ u} + 3.025995\text{ u}) - 6.01513\text{ u}\ \Delta m &= 6.047823\text{ u} - 6.01513\text{ u}\ \Delta m &= 0.032693\text{ u} \end{aligned} $$ ## Calculate the binding energy Using the *Nuclear Binding Energy* knowledge point $$ \begin{aligned} E_b &= \Delta m \times 931.5\text{ MeV/u}\ E_b &= 0.032693\text{ u} \times 931.5\text{ MeV/u}\ E_b &\approx 30.45\text{ MeV} \end{aligned} $$ The mass defect of the Lithium-6 nucleus is $0.032693\text{ u}$ and its binding energy is approximately $30.45\text{ MeV}$. { "subject": "Natural Science", "question_type": "Free Response", "knowledge_point": [ "Natural Science", "Physics", "Nuclear Binding Energy" ] }

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Explanation:

Identify the composition of Lithium-6

Calculate the mass defect

Calculate the binding energy

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