Respuesta :
Answer: The correct answer is Option D.
Explanation:
We are given a nucleus having representation: [tex]_6^{12}\textrm{C}[/tex]
Number of protons = 6
Number of neutrons = 12 - 6 = 6
Number of electrons = 6
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)+(n_e\times m_e)]-M[/tex]
where,
[tex]n_p[/tex] = number of protons = 6
[tex]m_p[/tex] = mass of one proton = 1.00728 u
[tex]n_n[/tex] = number of neutrons = 6
[tex]m_n[/tex] = mass of one neutron = 1.00866 u
[tex]n_e[/tex] = number of electrons = 6
[tex]m_e[/tex] = mass of one electron = 0.00054858 u
M = Mass number = 12
Putting values in above equation, we get:
[tex]\Delta m=[(6\times 1.00728)+(6\times 1.00866)+(6\times 0.00054858)]-12\\\\\Delta m=0.098931u[/tex]
To calculate the binding energy of the nucleus, we use the equation:
[tex]E=\Delta mc^2\\E=(0.098931u)\times c^2[/tex]
[tex]E=(0.098931u)\times (931.5MeV)[/tex] (Conversion factor: [tex]1u=931.5MeV/c^2[/tex] )
[tex]E=92.2MeV[/tex]
Hence, the correct answer is Option D.
