Determine the nuclear binding energy for Pd-101. atomic mass of Pd-101=100.908287 g/mol.
To determine the nuclear binding energy of an atom, you need to use Einstein's mass-energy equation, E=mc^2. You also need to know the mass defect, which is the difference between the actual mass of the atom and the sum of the masses of its protons, neutrons, and electrons.
To calculate the nuclear binding energy of Pd-101, follow these steps:
Step 1: Calculate the mass defect (Δm):
- Determine the total mass of the protons and neutrons in Pd-101. Since the atomic mass of Pd-101 is given as 100.908287 g/mol, we can assume it contains 102 particles (since the atomic number of palladium is 46).
- Calculate the mass of 102 protons and neutrons using the atomic mass unit (amu). The atomic mass unit is defined as 1/12th the mass of a carbon-12 atom, which is approximately 1.66 x 10^-27 kg.
- Mass of 102 particles = 102 amu x 1.66 x 10^-27 kg/amu
- Convert this mass to grams by multiplying by 1 g/10^-3 kg: mass of 102 particles = 102 amu x 1.66 x 10^-27 kg/amu x 1 g/10^-3 kg
Step 2: Calculate the nuclear binding energy (E):
- Use the mass defect (Δm) to calculate the energy using Einstein's equation, E = Δmc^2. The speed of light (c) is approximately 3 x 10^8 m/s.
- Nuclear binding energy = Δm x (3 x 10^8 m/s)^2
By performing these calculations, you can determine the nuclear binding energy for Pd-101.