The atomic masses of nitrogen-14, titanium-48, and xenon-129 are 13.999234, 47.9

Question

The atomic masses of nitrogen-14, titanium-48, and xenon-129 are 13.999234, 47.935878, and 128.904779 respectively. 1. For each isotope, calculate the nuclear mass. 2. For 14N,calculate he nuclear binding energy in 6 sig .figs. In joules 3. For 48Ti, calculate the nuclear binding energy in 6 sig. Figs in joules 4. For 129Xe, calculate the nuclear binding energy in 7 sig. Figs in joules 5. For 14N , calculate the nuclear binding energy per nucleon in Joules per nucleon in 6 sig. Figs 6. For 48Ti, calculate the nuclear binding energy per nucleon in 6 sig figs,also in joules. 7. For 129Xe, calculate the nuclear binding energy per nucleon in 7 sig.figs also in joules per nucleon.

Explanation / Answer

The He atom is composed of 2 protons, 2 neutrons and 2 electrons. The mass of 2 protons = 2 x 1.007277 amu The mass of 2 neutrons = 2 x 1.008665 amu The mass of 2 electrons = 2 x 0.0005486 amu The sum of the masses is 4.032981 amu The actual mass, as measured by a mass spectrometer, is 4.002603 amu. The difference (4.032981 - 4.002603) is 0.030378 amu For one mole of He atoms the difference would be 0.030378 grams Why is there a difference? If we were to break apart a He atom into protons, neutrons and electrons, a tremendous amout of evergy would be required. The amount of energy is called the binding energy. Obviously if we were to form a He atom from protons, neutrons, and electrons a tremendous amount of energy would be released. The amount of energy is equal to the binding energy. Where did the energy come from? Einstein showed that mass and energy are related by the equation E = mc^2.. Using the speed of light, c, of 2.9979x10^8 m/s and the mass that was lost when the He was formed (3.0378x10^-5 kg) the calculated binding energy is 2.7302x10^12 kg m^2 s^2. 1 joule = 1 kg m^2 s^2 so the binging energy of 1 mol He = 2.73x10^12 J/mol or 2.73x10^9 kJ/mol. The binding energy is usually expressed in energy units of Mev (1 million electron volts). 931 MeV is approximately equal to the mass of 1 amu. Thus, the mass of 0.030378 amu = 931 x 0.030378 = 28.3 MeV The binding energy of a He atom is 28.3 MeV The He atom is composed of 4 nucleons (2 protons + 2 neutrons), so the average binding energy per nucleon is 28.3 MeV/4 = 7.07 MeV. The average bindfing energy per nucleon varies for different atoms.

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