Respuesta :
Answer : The nuclear binding energy of He for one mole is [tex]2.0\times 10^{12}J/mol[/tex]
Explanation :
The isotopic representation of He : [tex]_{2}^{4}\textrm{He}[/tex]
Atomic number = Number of protons = 2
Mass number = 4
Number of neutrons = Mass number - Atomic number = 4 - 2 = 2
To calculate the mass defect of the nucleus, we use the equation:
[tex]\Delta m=[(n_p\times m_p)+(n_n\times m_n)+]-M[/tex]
where,
[tex]n_p[/tex] = number of protons = 2
[tex]m_p[/tex] = mass of one proton = 1.00728 amu
[tex]n_n[/tex] = number of neutrons = 2
[tex]m_n[/tex] = mass of one neutron = 1.00866 amu
M = Nuclear mass number = 4.00150 amu
Putting values in above equation, we get:
[tex]\Delta m=[(2\times 1.00728)+(2\times 1.00866)]-[4.00150]\\\\\Delta m=0.03038amu[/tex]
Now converting the value of amu into kilograms, we use the conversion factor:
[tex]1amu=1.66\times 10^{-27}kg[/tex]
So, [tex]0.03038amu=0.03038\times 1.66\times 10^{-27}kg=0.0504\times 10^{-27}kg[/tex]
To calculate the equivalent energy, we use the equation:
[tex]E=\Delta mc^2[/tex]
E = nuclear binding energy = ?
[tex]\Delta m[/tex] = mass change = [tex]0.0504\times 10^{-27}kg[/tex]
c = speed of light = [tex]3\times 10^8m/s[/tex]
Putting values in above equation, we get:
[tex]E=(0.0504\times 10^{-27}kg)\times (3.0\times 10^8m/s)^2\\\\E=4\times 10^{-12}J[/tex]
Nuclear binding energy for one mole is:
[tex]E=(4.0\times 10^{-12}J)\times (6.022\times 10^{23}mol^{-1})=2.0\times 10^{12}J/mol[/tex]
Therefore, the nuclear binding energy of He for one mole is [tex]2.0\times 10^{12}J/mol[/tex]
