Nuclear Physics

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Atomic number (Z) is the number of protons in the nucleus. Mass number (A) is the total number of protons and neutrons (nucleons) in the nucleus. For example, in \( {}_{92}^{238}\mathrm{U} \), Z = 92 …

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Isotopes: Atoms of same element (same Z) but different mass numbers (A). Example: \( {}_{6}^{12}\mathrm{C} \) and \( {}_{6}^{14}\mathrm{C} \). Isobars: Atoms with same A but different Z. Example: \( {…

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Number of neutrons = A – Z. For \( {}_{13}^{27}\mathrm{Al} \): N = 27 – 13 = 14. For \( {}_{14}^{28}\mathrm{Si} \): N = 28 – 14 = 14. So both have 14 neutrons.

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The radius R of a nucleus is given by: \( R = r_0 A^{1/3} \), where \( r_0 = 1.2 imes 10^{-15} \, ext{m} \) (1.2 fm). For example, for A = 8, \( R = 1.2 imes 8^{1/3} = 1.2 imes 2 = 2.4 \, ext{fm}…

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Given: \( R = r_0 A^{1/3} \), \( r_0 = 1.2 imes 10^{-15} \, ext{m} \), A = 8. Step 1: \( A^{1/3} = 8^{1/3} = 2 \). Step 2: \( R = 1.2 imes 10^{-15} imes 2 = 2.4 imes 10^{-15} \, ext{m} \). Answe…

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1 u = 1/12th the mass of a \( {}_{6}^{12}\mathrm{C} \) atom = \( 1.660565 imes 10^{-27} \, ext{kg} \). Using \( E = mc^2 \), 1 u = 931.3 MeV. This is used to express nuclear masses and calculate bin…

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Mass defect (\( \Delta m \)) is the difference between the sum of masses of individual nucleons and the actual mass of the nucleus. Formula: \( \Delta m = [Z m_p + (A-Z) m_n] - M \), where M is the ac…

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Given: \( m_p = 1.00727 \, ext{u} \), \( m_n = 1.00865 \, ext{u} \), A = 7, Z = 3. Step 1: Sum of nucleon masses = \( 3(1.00727) + 4(1.00865) = 3.02181 + 4.0346 = 7.05641 \, ext{u} \). Step 2: Mass…