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

atomic number of Ir = # of protons = 77

so
mass of protons = 77.56056 amu
mass of neutrons = 110.9526 amu
total mass = 188.51316 amu

188.51316 - 187.95883 = .55433 grams/mol

= .00055433 kg/mol

* c^2 for energy /mol

.00055433 kg/mol * 9 * 10^16
= .00498897 *10^16 Joules/mol
divide by Avagadro # for Joules per nucleus
.00498897 *10^16 Joules/mol/(6*10^23)
= .005 * 10^-7
= 5 * 10^-4 Joules/nucleus

the answer is -4.43E-12 J/nucleons

I believe that answer should be -4.43E-13 J/nucleon.

0.55433 amu x 1.6605E-27 kg/amu x c^2 = ? for 187 nucleons. Divide by 187 for 4.42E-13 J/nucleon.

how u know to divide by 1.66E-27

so how do you solve it again?

To calculate the nuclear binding energy of Ir-187, you need to use the equation E = mc², where E represents energy, m represents mass, and c is the speed of light.

1. First, calculate the total mass of Ir-187 by adding up the masses of protons and neutrons:
Mass of proton = 1.00728 amu
Mass of neutron = 1.00866 amu
Atomic mass of Ir-187 = 187.958830 g/mol

Number of protons (Z) = atomic number of Ir = 77
Number of neutrons (N) = atomic mass - atomic number = 187 - 77 = 110

Total mass of Ir-187 = (number of protons * mass of proton) + (number of neutrons * mass of neutron)
= (77 * 1.00728 amu) + (110 * 1.00866 amu)

2. Next, convert the total mass from amu (atomic mass units) to grams (g) by using Avogadro's number, which states that there are 6.0221 × 10^23 amu in 1 gram:
Total mass of Ir-187 (g) = (Total mass of Ir-187 in amu) / Avogadro's number
= (Total mass of Ir-187 in amu) / (6.0221 × 10^23 amu/g)

3. Now, multiply the total mass of Ir-187 (g) by the square of the speed of light (c²) to obtain the nuclear binding energy.
Nuclear binding energy (per nucleon) = (Total mass of Ir-187 in g) * (speed of light)^2

Remember that the speed of light is approximately 3.00 × 10^8 meters per second (m/s).