Let's clarify the question first: - **H-3 (Hydrogen-3 or Tritium)**: This is an isotope hydrogen with 1 proton and 2 neutrons. - **C-4 (Carbon-4)**: This is an isotope of carbon with 6 protons and 4 neutrons. You are asked to **find \( B_1 \) and \( B_2 \)**. Usually, in nuclear chemistry, \( B \) stands for **binding energy**. Let's proceed step by step. --- # Step 1: Find Mass Numbers and Atomic Numbers | Isotope | Symbol | Atomic Number (\( Z \)) | Neutron Number (\( N \)) | Mass Number (\( A \)) | |---------|--------|------------------------|--------------------------|-----------------------| | H-3 | \( ^3_1\text{H} \) | 1 | 2 | 3 | | C-4 | \( ^4_6\text{C} \) | 6 | -2 | 4 | **Note:** C-4 is very unstable and rare; it has more protons than neutrons. --- # Step 2: Write Formula for Binding Energy The **binding energy** (\( B \)) is calculated as: \[ B = \left[ Z m_p + N m_n - M_{\text{atom}} \right] c^2 \] Where: - \( m_p \) = mass of a proton - \( m_n \) = mass of a neutron - \( M_{\text{atom}} \) = actual mass of the atom (from mass tables) - \( c \) = speed of light (usually, mass is in atomic units and \( c^2 \) is absorbed into units of MeV) **For calculation in MeV:** \[ B = \left( \text{mass defect in u} \right) \times 931.5 \ \text{MeV} \] --- # Step 3: Gather Atomic Masses | Particle | Mass (u) | |----------|----------------| | Proton | 1.007825 u | | Neutron | 1.008665 u | | Electron | .0005486 u | **Actual atomic masses:** - Tritium (\( ^3_1\text{H} \)): \( 3.016049 \) u - Carbon-4 (\( ^4_6\text{C} \)): \( 4.003241 \) u --- # Step 4: Calculate Binding Energy for H-3 (\( B_1 \)) ### 1. Calculate total mass of separate nucleons: \[ \text{Protons:} \ 1 \times 1.007825 = 1.007825~\text{u} \] \[ \text{Neutrons:} \ 2 \times 1.008665 = 2.017330~\text{u} \] \[ \text{Electrons:} \ 1 \times .0005486 = .0005486~\text{u} \] \[ \text{Total (separate)} = 1.007825 + 2.017330 + .0005486 = 3.0257036~\text{u} \] ### 2. Subtract actual atomic mass: \[ \text{Mass defect} = 3.0257036 - 3.016049 = .0096546~\text{u} \] ### 3. Calculate binding energy: \[ B_1 = .0096546~\text{u} \times 931.5~\frac{\text{MeV}}{\text{u}} = 9.00~\text{MeV} \] --- # Step 5: Calculate Binding Energy for C-4 (\( B_2 \)) ### 1. Calculate total mass of separate nucleons: \[ \text{Protons:} \ 6 \times 1.007825 = 6.046950~\text{u} \] \[ \text{Neutrons:} \ (-2) \times 1.008665 = -2.017330~\text{u} \] (But a nucleus cannot have negative neutrons. C-4 is not possible with 6 protons and 4 nucleons; likely, the intended isotope is \( ^4_2\text{He} \), which is an alpha particle.) ## **If you meant "C-4" as Carbon-4 (\( ^4_6\text{C} \))**, it can't exist (mass number 4, proton number 6), so **binding energy is not defined**. --- # Step 6: Summary Table | Isotope | Binding Energy (\( B \)) | |---------|--------------------------| | H-3 | \( 9.00~\text{MeV} \) | | C-4 | *Not defined / impossible* | --- # Final Answers **For H-3 (Tritium):** \[ \boxed{B_1 = 9.~\text{MeV}} \] **For C-4:** \[ \boxed{B_2 = \text{Not defined, as C-4 is not a possible isotope}} \] --- ## Note If you meant a different isotope for "C-4", please clarify. If you meant \( ^4_2\text{He} \) (Helium-4), let me know and I can calculate its binding energy as well.