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 each isotope, calculate (a) the nuclear mass, (b) the nuclear binding energy, (c) the nuclear binding energy per nucleon. (d) Which of these three isotopes has the largest nuclear binding energy per nucleon? Does this agree with the trends plotted in Figure 21.12\(?\)

First, let's find the nuclear masses for each isotope. We can do this by multiplying the atomic mass units (amu) by the conversion factor to get the mass in kg. Conversion factor: 1 amu = 1.66054 x 10^-27 kg For hydrogen-2 (deuterium): Atomic mass = 2.014102 amu Nuclear mass = 2.014102 amu * (1.66054 x 10^-27 kg/amu) = 3.34399 x 10^-27 kg For helium-4: Atomic mass = 4.002602 amu Nuclear mass = 4.002602 amu * (1.66054 x 10^-27 kg/amu) = 6.64412 x 10^-27 kg For lithium-6: Atomic mass = 6.0151228 amu Nuclear mass = 6.0151228 amu * (1.66054 x 10^-27 kg/amu) = 9.98864 x 10^-27 kg

Next, we'll calculate the nuclear binding energy for each isotope using the formula: Nuclear binding energy = (Z * mass_H + N * mass_n - nuclear_mass) * c^2 where Z: number of protons, mass_H: mass of a proton (1.007825 amu), N: number of neutrons, mass_n: mass of a neutron (1.008665 amu), c: speed of light (3 x 10^8 m/s) For hydrogen-2: Z = 1, N = 1 Binding energy = [(1 * 1.007825) + (1 * 1.008665) - 2.014102] * (1.66054 x 10^-27 kg/amu) * (3 x 10^8 m/s)^2 Binding energy = 2.224 x 10^-13 J For helium-4: Z = 2, N = 2 Binding energy = [(2 * 1.007825) + (2 * 1.008665) - 4.002602] * (1.66054 x 10^-27 kg/amu) * (3 x 10^8 m/s)^2 Binding energy = 4.0323 x 10^-12 J For lithium-6: Z = 3, N = 3 Binding energy = [(3 * 1.007825) + (3 * 1.008665) - 6.0151228] * (1.66054 x 10^-27 kg/amu) * (3 x 10^8 m/s)^2 Binding energy = 3.2994 x 10^-12 J

Now, we'll find the nuclear binding energy per nucleon for each isotope by dividing the nuclear binding energy by the number of nucleons (protons + neutrons). For hydrogen-2: Binding energy per nucleon = (2.224 x 10^-13 J) / 2 = 1.112 x 10^-13 J/nucleon For helium-4: Binding energy per nucleon = (4.0323 x 10^-12 J) / 4 = 1.008075 x 10^-12 J/nucleon For lithium-6: Binding energy per nucleon = (3.2994 x 10^-12 J) / 6 = 5.499 x 10^-13 J/nucleon

Comparing the nuclear binding energy per nucleon for each isotope: Hydrogen-2: 1.112 x 10^-13 J/nucleon Helium-4: 1.008075 x 10^-12 J/nucleon Lithium-6: 5.499 x 10^-13 J/nucleon Helium-4 has the largest nuclear binding energy per nucleon, with a value of 1.008075 x 10^-12 J/nucleon.

We're unable to view Figure 21.12, but the general trend typically shows an increase in nuclear binding energy per nucleon as the atomic number increases, reaching a peak around the atomic number of iron. Our result of helium-4 having the largest binding energy per nucleon among the three given isotopes is expected based on its higher atomic number compared to hydrogen-2. For the lithium-6 isotope, it doesn't follow the general trend for lighter elements because its atomic mass is relatively higher than helium-4. This may cause some deviations, which might be evident in Figure 21.12.