determine the nuclear binding energy for Ir-187. Atomic mass of Ir-187=187.958830 g/mol

(per nucleon)

dE=dmc(^2)

mass of proton= 1.00728 amu
mass of neutron=1.00866 amu

To determine the nuclear binding energy for Ir-187, you can use the equation E = Δmc², where E represents the nuclear binding energy, Δm represents the mass defect, and c represents the speed of light (3.00 x 10^8 m/s).

To calculate the mass defect (Δm), you need to subtract the mass of Ir-187 from the combined mass of its protons and neutrons.

Let's start by calculating the combined mass of the protons and neutrons in Ir-187:

Number of protons = atomic number = 77
Number of neutrons = mass number - number of protons
= 187 - 77
= 110

Now, calculate the combined mass of protons and neutrons:

Mass of protons = (mass of proton) × (number of protons)
= 1.00728 amu × 77
= 77.71656 amu

Mass of neutrons = (mass of neutron) × (number of neutrons)
= 1.00866 amu × 110
= 110.9526 amu

Combined mass of protons and neutrons = mass of protons + mass of neutrons
= 77.71656 amu + 110.9526 amu
= 188.66916 amu

Now, calculate the mass defect:

Mass defect (Δm) = Combined mass of protons and neutrons - Mass of Ir-187
= 188.66916 amu - 187.958830 g/mol
= 0.71033 amu

Finally, calculate the nuclear binding energy (E):

Nuclear binding energy (E) = Δmc²
= (0.71033 amu) × (1.6605 × 10^(-27) kg/amu) × (3.00 × 10^8 m/s)²
≈ 1.199 × 10^(-11) J

Therefore, the nuclear binding energy per nucleon for Ir-187 is approximately 1.199 × 10^(-11) J.