There are three isotopes of phosphorus. Only one of them is stable. Calculate the binding energy per nucleon (in MeV) for P-32 (atomic mass = 31.9739 u). mass H = 1.007825 u and mass n = 1.008665 u.
I multiplied the protons(15) by the mass H, and the neutrons(16) by the mass n. Then I subtracted the atomic mass(31.9739) by the calculated mass and got -.717885 amu and then I used E=mc^2 to find the energy and I divided that energy by 32, my final answer was 2.02e15 but its wrong.
You need to convert amu to kg. You can look up the factor on Google. E will come out in joules and you convert that to MeV.
To calculate the binding energy per nucleon (BE/A) for an isotope, you need to use the mass defect and the mass of the isotope.
First, let's calculate the mass defect:
1. Multiply the number of protons (Z) by the mass of a hydrogen atom (H) to get the total mass of the protons.
Mass of protons = Z * mass H = 15 * 1.007825 u = 15.117375 u
2. Multiply the number of neutrons (N) by the mass of a neutron (n) to get the total mass of the neutrons.
Mass of neutrons = N * mass n = 16 * 1.008665 u = 16.13864 u
3. Add the mass of protons and neutrons.
Total mass of nucleons = Mass of protons + Mass of neutrons = 15.117375 u + 16.13864 u = 31.256015 u
4. Calculate the mass defect by subtracting the atomic mass from the total mass of nucleons.
Mass defect = Total mass of nucleons - Atomic mass = 31.256015 u - 31.9739 u = -0.717885 u
Next, let's calculate the binding energy:
1. Convert the mass defect from atomic mass units (u) to kilograms (kg).
1 u = 1.66053906660 x 10^-27 kg
Mass defect in kg = -0.717885 u * (1.66053906660 x 10^-27 kg/u) = -1.192194 x 10^-27 kg
2. Use Einstein's mass-energy equation, E = mc^2, to calculate the energy.
Energy (E) = Mass defect * c^2
c = 2.998 x 10^8 m/s (speed of light in a vacuum)
Energy (E) = (-1.192194 x 10^-27 kg) * (2.998 x 10^8 m/s)^2
3. Convert the energy from joules (J) to mega-electron volts (MeV).
1 MeV = 1.60219 x 10^-13 J
Energy in MeV = Energy (in J) / (1.60219 x 10^-13 J/MeV)
Finally, divide the binding energy by the number of nucleons (A) to get the binding energy per nucleon:
BE/A = Energy in MeV / A
Using the values provided, the calculation should yield the correct answer.