Question

an atom of 135i has a mass of 134.910023 amu. calculate its binding energy per mole in kj. enter your answer in exponential format (1.23e4) with 3 significant figures and no units. use the masses: mass of 1h atom

Answer 1

To calculate the binding energy per mole of 135I, we need to first determine its mass defect (Δm) using the atomic masses of its constituents:

Mass of 135I atom = 134.910023 amu

Mass of 53 protons = 53 x 1.007825 amu = 53.421325 amu

Mass of 82 neutrons = 82 x 1.008665 amu = 82.82893 amu

Total mass of 135I nucleus = 53.421325 amu + 82.82893 amu = 136.250255 amu

Δm = (mass of 135I atom) - (total mass of 135I nucleus)

= 134.910023 amu - 136.250255 amu

= -1.340232 amu

The binding energy (BE) can be calculated from the mass defect using Einstein's famous equation:

BE = Δm x c^2

where c is the speed of light in a vacuum (299,792,458 m/s).

BE = -1.340232 amu x (1.66054 x 10^-27 kg/amu) x (299,792,458 m/s)^2 / (6.02214 x 10^23 atoms/mol) / 1000 J/kJ

= -2.2008 x 10^-11 J/atom

Multiplying by Avogadro's number (6.02214 x 10^23 atoms/mol) gives the binding energy per mole:

BE/mol = -2.2008 x 10^-11 J/atom x (6.02214 x 10^23 atoms/mol) / 1000 J/kJ

= -1.3241 x 10^4 kJ/mol

Rounding to 3 significant figures and expressing in exponential format gives the final answer of -1.32e4 kJ/mol.

Step-by-step explanation:

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