Respuesta :
Answer:
[tex]1.365\times10^{-12}\ J/nucleon[/tex]
Explanation:
Given [tex]^{86}sr[/tex] has mass of 85.9094 amu.
We will find theoretical mass of Strontium nucleus
We know Strontium has [tex]38\ protons[/tex]
and [tex](86-38)=48\ neutrons[/tex]
Also, mass of neutron is [tex]1.0087\ amu[/tex]
and mass of proton is [tex]1.0073\ amu[/tex]
So, theoretical mass of Strontium nucleus[tex] = [/tex]Mass of a proton[tex] + [/tex]Mass of a neutron
[tex](38\times1.0073)+(48\times1.0087)\\=38.2774+48.4176\\=86.695\ amu[/tex]
Actual Strontium nuclear mass is [tex]85.9094\ amu[/tex] (Given)
So, mass defect will be
[tex]86.69 -85.9094=0.7856\ amu[/tex]
[tex]1\ amu=1g/mol\\1g/mol=1.6605\times10^{-24}\ g/atom\\\\(0.7856\ g/mol)\times(1.6605\times10^{-24}\ atom/mol)\times(\frac{1}{86}\ nucleons/atom)\\=1.5169\times10^{-26}\ g/nucleon\\\\We\ know\ 1g=10^{-3}\ Kg\\\\So,\ 1.5169\times10^{-26}\ g/nucleon=1.5169\times10^{-29}\ Kg/nucleon[/tex]
Also, [tex]E=mc^2\\Where\ c\ is\ speed\ of\ light\ in\ vaccum=3\times10^8\\m\ is\ mass\\And\ E\ is\ energy[/tex]
[tex]E=1.5169\times10^{-29}(3\times10^8)^2\\\\=1.365\times10^{-12}\ J/nucleon[/tex]
