Question

What is the binding energy of potassium-35 when the atomic mass is determined to be 34.88011 amu?

Answer 1

The binding energy of an atomic nucleus can be calculated using Einstein's mass-energy equivalence equation, E = mc², where E is the binding energy, m is the mass defect, and c is the speed of light.

To determine the binding energy of potassium-35, we need the exact atomic mass of potassium-35 and the atomic mass unit (amu) conversion factor. Since the atomic mass given is already in amu, we can proceed with the calculation.

The mass defect (Δm) is the difference between the actual mass of the nucleus and the sum of the masses of its individual protons and neutrons. It can be calculated as follows:

Δm = Atomic mass of potassium-35 - (Number of protons × mass of a proton) - (Number of neutrons × mass of a neutron)

Since potassium has 19 protons and 16 neutrons:

Δm = 34.88011 amu - (19 × mass of a proton) - (16 × mass of a neutron)

The mass of a proton is approximately 1.007276 amu, and the mass of a neutron is approximately 1.008665 amu. Substituting these values into the equation:

Δm = 34.88011 amu - (19 × 1.007276 amu) - (16 × 1.008665 amu)

After calculating the value of Δm, the binding energy (E) can be obtained by multiplying the mass defect by the square of the speed of light (c²), where c ≈ 2.998 × 10^8 m/s.

Please note that the actual calculation may require a higher precision value for the atomic mass and the masses of the proton and neutron.

Answer 2

The binding energy of potassium-35 can be calculated using the formula:
Ebinding = (Δm) × (c^2)
where Δm is the mass defect and c is the speed of light. The mass defect is calculated as follows:
Δm = (Z × mp + N × mn − m)
where Z is the atomic number, mp is the mass of a proton, N is the number of neutrons, mn is the mass of a neutron, and m is the atomic mass.
For potassium-35 with an atomic mass of 34.88011 amu, we have:
Z = 19 N = 16 mp = 1.00728 u mn = 1.00867 u m = 34.88011 u
Δm = (19 × 1.00728 u + 16 × 1.00867 u − 34.88011 u) = 0.299288 u
Using the conversion factor that 1 u of mass defect involves about 931.5 MeV of binding energy, we get:
Ebinding = Δm × c^2 = (0.299288 u) × (931.5 MeV/u) × (c^2) = 278.79 MeV1.
Therefore, the binding energy of potassium-35 when the atomic mass is determined to be 34.88011 amu is approximately 278.79 MeV