Final answer:
The binding energy in an atom of 3He can be calculated using the mass defect and the mass-energy equivalence equation.
Step-by-step explanation:
The binding energy in an atom of 3He can be calculated using the mass defect and the mass-energy equivalence equation. The mass defect for a 3He nucleus is the difference between the mass of the nucleus (3.016030 amu) and the sum of the masses of its constituent particles (2 protons and 1 neutron).
Step 1: Calculate the mass defect. The mass of the 3He nucleus is 3.016030 amu. The mass of 2 protons is 2 × 1.007825 amu = 2.01565 amu. The mass of 1 neutron is 1.008665 amu. Therefore, the mass defect is:
Mass defect = (3.016030 amu) - (2 × 1.007825 amu + 1.008665 amu) = 3.016030 amu - 2.024315 amu = 0.991715 amu.
Step 2: Convert the mass defect to energy using the mass-energy equivalence equation E = mc², where E is the energy, m is the mass defect, and c is the speed of light.
Since the mass defect must be expressed in kilograms for the equation, we need to convert amu to kilograms. The conversion factor is 1 amu = 1.66053906660 x 10⁻²⁷ kg. Therefore, the mass defect in kilograms is:
Mass defect in kg = 0.991715 amu × 1.66053906660 x 10⁻²⁷ kg/amu) = 1.644070093 x 10⁻²⁷ kg.
Now we can calculate the binding energy using the mass-energy equivalence equation:
Binding energy = (mass defect in kg) × c².
Since the speed of light, c, is approximately 2.998 x 10^8 m/s, we can calculate the binding energy:
Binding energy = (1.644070093 x 10⁻²⁷ kg) × (2.998 x 10⁸ m/s)² = 1.480394756 x 10⁻¹⁰ J.
Finally, we can convert the binding energy from joules to millielectron volts (MeV) using the conversion factor 1 MeV = 1.60218 x 10⁻¹³ J:
Binding energy = (1.480394756 x 10⁻¹⁰ J) × (1 MeV/1.60218 x 10⁻¹³ J) = 0.923615105 MeV.
Therefore, the binding energy in an atom of 3He is approximately 0.9236 MeV.