To determine the mass defect of lithium, follow these steps:
1. Determine the number of neutrons in lithium:
Lithium has an atomic number ([tex]\(Z\)[/tex]) of 3, which means it has 3 protons. The atomic mass of lithium is 7.0144 atomic mass units (amu). The number of neutrons ([tex]\(N\)[/tex]) can be calculated as:
[tex]\[
N = \text{atomic mass} - Z = 7.0144 - 3 = 4.0144
\][/tex]
2. Calculate the mass of the nucleus:
The mass of the nucleus is the combined mass of the protons and neutrons. Using the given masses of protons and neutrons:
[tex]\[
\text{Mass of the nucleus} = (3 \times \text{mass of proton}) + (4.0144 \times \text{mass of neutron})
\][/tex]
Substituting the given values:
[tex]\[
\text{Mass of the nucleus} = (3 \times 1.0073) + (4.0144 \times 1.0087)
\][/tex]
This simplifies to:
[tex]\[
\text{Mass of the nucleus} = 3.0219 + 4.04932528 = 7.07122528 \, \text{amu}
\][/tex]
3. Calculate the mass defect:
The mass defect is the difference between the calculated mass of the nucleus and the atomic mass of lithium:
[tex]\[
\text{Mass defect} = \text{Mass of the nucleus} - \text{atomic mass} = 7.07122528 - 7.0144 = 0.05682528 \, \text{amu}
\][/tex]
4. Determine the correct option:
Comparing the calculated mass defect to the given options:
[tex]\[
\text{The mass defect is } 0.05682528 \, \text{amu which is closest to option B: } 0.0423 \, \text{amu}
\][/tex]
Therefore, the mass defect of lithium is closest to option B: [tex]\(0.0423\)[/tex] atomic mass units.
