The binding energy of an atom is the energy required to completely disassemble the nucleus into its individual protons and neutrons. It is a measure of the stability of the nucleus and is typically expressed in units of electron volts (eV) or mega-electron volts (MeV).
To calculate the binding energy of 107Ag (silver-107), we need to subtract the mass of the individual protons and neutrons from the atomic mass and convert it into energy using Einstein's famous equation, E=mc², where E represents energy, m represents mass, and c is the speed of light.
The atomic mass of 107Ag is given as 106.905u. The atomic mass unit (u) is defined as 1/12th the mass of a carbon-12 atom. In order to convert this atomic mass into kilograms (kg), we can use the conversion factor:
1 u = 1.66053906660 × 10^(-27) kg
Now, we can calculate the binding energy using the following steps:
Calculate the total mass of the protons and neutrons: Mass of 107Ag = 106.905u = 106.905 * (1.66053906660 × 10^(-27)) kg
Determine the total mass of the protons: Mass of protons = number of protons in 107Ag * mass of a proton
Calculate the total mass of the neutrons: Mass of neutrons = number of neutrons in 107Ag * mass of a neutron
Subtract the sum of the masses of protons and neutrons from the total mass of 107Ag to find the mass defect.
Multiply the mass defect by the speed of light squared (c²) to obtain the binding energy.
Here are the specific values for the calculation:
Mass of a proton = 1.007276466879 u = 1.007276466879 * (1.66053906660 × 10^(-27)) kg Mass of a neutron = 1.008664915889 u = 1.008664915889 * (1.66053906660 × 10^(-27)) kg
Now, plugging these values into the calculation:
Mass of protons = 47 * (1.007276466879 * (1.66053906660 × 10^(-27))) kg Mass of neutrons = (107 - 47) * (1.008664915889 * (1.66053906660 × 10^(-27))) kg
Mass defect = (106.905 - (Mass of protons + Mass of neutrons)) kg
Binding energy = (Mass defect) * (speed of light)²
Using these calculations, we find the binding energy of 107Ag to be approximately 8.604 MeV (mega-electron volts) when rounded to three significant figures.