Writing equation for constituents of given nuclei
#"_7^15##"N"=7p+8n-BE_N# .......(1)
#"_8^15##"O"=8p+7n-BE_O# .......(2)
where #p# is proton, #n# neutron and #BE# is binding energy of nucleus. When constituents of nucleus are brought together binding energy is released.
Subtracting (1) from (2)
#"O"-"N"=8p+7n-BE_O-(7p+8n-BE_N)#
#=>"O"-"N"=p-n-DeltaBE#
Inserting given values we get
#15.003065-15.000109=1.007825-1.008665-DeltaBE#
#=>0.002956=-0.00084-DeltaBE#
#=>-DeltaBE=0.003796=3.535974Mev# ......(3)
Given electrostatic energy of nucleus is
#E=3/5(Z(Z-1)e^2)/(4piepsilon_0R)#
Calculating respective electrostatic energies we get
#E_"O"=3/5(8(8-1)e^2)/(4piepsilon_0R)# ......(4)
#E_"N"=3/5(7(7-1)e^2)/(4piepsilon_0R)# .......(5)
As difference of binding energy is purely due to electrostatic energy, therefore, we have
#DeltaBE=E_"N"-E_"O"#
Inserting values from equations (3), (4) and (5) and absorbing #-ve# sign we get
#3.535974=3/5(8(8-1)e^2)/(4piepsilon_0R)-3/5(7(7-1)e^2)/(4piepsilon_0R)#
#=>3.535974=3/5xx[8(8-1)-7(7-1)]xx((e^2)/(4piepsilon_0R))#
#=>3.535974=3/5xx14xx1.44xx1/R#
#=>R=3/5xx14xx1.44xx1/3.535974#
#=>R=3.42fm#
