Question

The nuclide sr-86 has a mass of 85.9094 u. What is the binding energy per nucleon for this nuclide?

Answer 1

Answer:

$1.365\times10^{-12}\ J/nucleon$

Explanation:

Given $^{86}sr$ has mass of 85.9094 amu.

We will find theoretical mass of Strontium nucleus

We know Strontium has $38\ protons$

and $(86-38)=48\ neutrons$

Also, mass of neutron is $1.0087\ amu$

and mass of proton is $1.0073\ amu$

So, theoretical mass of Strontium nucleus$=$Mass of a proton$+$Mass of a neutron

$(38\times1.0073)+(48\times1.0087)\\=38.2774+48.4176\\=86.695\ amu$

Actual Strontium nuclear mass is $85.9094\ amu$ (Given)

So, mass defect will be

$86.69 -85.9094=0.7856\ amu$

$1\ amu=1g/mol\\1g/mol=1.6605\times10^{-24}\ g/atom\\\\(0.7856\ g/mol)\times(1.6605\times10^{-24}\ atom/mol)\times(\frac{1}{86}\ nucleons/atom)\\=1.5169\times10^{-26}\ g/nucleon\\\\We\ know\ 1g=10^{-3}\ Kg\\\\So,\ 1.5169\times10^{-26}\ g/nucleon=1.5169\times10^{-29}\ Kg/nucleon$

Also, $E=mc^2\\Where\ c\ is\ speed\ of\ light\ in\ vaccum=3\times10^8\\m\ is\ mass\\And\ E\ is\ energy$

$E=1.5169\times10^{-29}(3\times10^8)^2\\\\=1.365\times10^{-12}\ J/nucleon$