The atomic masses of hydrogen-2 (deuterium), heliu...

Question

The atomic masses of hydrogen-2 (deuterium), helium-4, and lithium-6 are 2.014102 amu, 4.002602 amu, and 6.0151228 amu, respectively. A graph shows that binding energy increases rapidly, levels off, and then declines slowly.

For ⁶Li, calculate the nuclear binding energy in mega electronvolts (MeV) per nucleon.

Jules Bruno · Accepted Answer

We are asked to calculate the nuclear binding energy in mega electronvolts (MeV) per nucleon for  6Li which has an atomic mass of 6.0151228 amuNuclear binding energy is the minimum energy that would be required to disassemble the nucleus of an atom into its component parts. These component parts are neutrons and protons, which are collectively called nucleonsTo calculate for the nuclear binding energy:Step 1: Determine the number of protons and neutronsStep 2: Determine the theoretical massStep 3: Calculate the mass defect (∆m)Step 4: Determine nuclear binding energy per nucleon[readmore]Step 1: Determine the number of protons and neutronsRecall the atomic number of an element is equal to the number of protons and that the atomic mass or mass number is the sum of protons and neutrons. Atomic mass = # of protons + # or neutronsFor 6Li:Atomic number = number or protons = 3Atomic mass = # of protons = 6.0151228 amu ≈ 6 amu6 = 3 + # of neutrons6 - 3 = # of neutrons# of neutrons = 3Step 2: Determine the theoretical mass6Li has 6 protons and 3 neutrons. We calculate the theoretical mass that is given by the equation:Theoretical mass = mass proton + mass neutronGiven:• mass neutron = 1.008665 amu• mass proton = 1.0072764 amu• number of protons = 6• number of neutrons = 3Plugin the values and calculate the theoretical massTheoretical mass = mass proton + mass neutronTheoretical mass = 6 (1.0072764 amu) + 3 (1.008665 amu)Theoretical mass = 6.0436584 amu + 3.025995 amuTheoretical mass = 9.0696534 amuStep 3: Calculate the mass defect (∆m)We calculate the mass defect that is given by the equation:∆m = theoretical mass - actual massGiven:• theoretical mass = 9.0696534 amu• actual mass = 6.0151228 amuPlugin the values and calculate the mass defect ∆m = theoretical mass - actual mass∆m = 9.0696534 amu - 6.0151228 amu∆m = 3.0545306 amuStep 4: Determine nuclear binding energy per nucleon We first calculate for the binding energy. The mass defect of 6Li is 3.054306 amu. Recall that 1 amu releases 931.5 MeV energy, soBinding energy =∆m(931.5 MeVamu)Binding energy = (3.0545306 amu)(931.5 MeVamu)Binding energy = 2845.295254 MeV Now, we calculate the binding energy per nucleon• Nucleons refer to both protons and neutrons. In other words, it is the atomic mass. The atomic mass of 6Li is 6. So the number of nucleons of 6Li is 6.Binding energy# nucleons=2845.295254 MeV6 nucleons = 474.22 MeV/nucleonThe nuclear binding energy of 6Li is 474.22 MeV/nucleon

Problem: The atomic masses of hydrogen-2 (deuterium), helium-4, and lithium-6 are 2.014102 amu, 4.002602 amu, and 6.0151228 amu, respectively. For 6Li, calculate the nuclear binding energy in mega electronvolts (MeV) per nucleon.

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Problem: The atomic masses of hydrogen-2 (deuterium), helium-4, and lithium-6 are 2.014102 amu, 4.002602 amu, and 6.0151228 amu, respectively. For 6Li, calculate the nuclear binding energy in mega electronvolts (MeV) per nucleon.

FREE Expert Solution

Problem Details

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