Question

please explain in detail

Determine the binding energy for a 12C nucleus assuming a mass of 12.000 amu. Proton mass = 1.007276amu,Neutronmass=1.008665amu,c=3x108 ms-1,1amu=1.66054x10-24 gand1J= 1 kg m2 s-2

a. 7 x 107 J
b. 1.43 x 10-8 J
c. 1.43 x 10-11 J
d. 7.00 x 1010 J
e. 8.61 x 1012 J

Answer 1

Correct answer is (c.) 1.43 x 10^-11 J

Explanation

A ¹²C nucleus contains 6 protons and 6 neutrons

mass of 6 protons = 6 * mass of 1 proton

mass of 6 protons = 6 * 1.007276 amu

mass of 6 protons = 6.043656 amu

similarly mass of 6 neutrons = 6.05199 amu

Total mass of neutrons and protons = 6.043656 amu + 6.05199 amu

Total mass = 12.095646 amu

change in mass = Total mass - mass of ¹²C nucleus

change in mass = 12.095646 amu - 12.000 amu

change in mass = 0.095646 amu

change in mass (kg) = 0.095646 amu * (1.66054 x 10^-24 g / 1 amu ) * (1 kg / 1000 g)

change in mass (kg) = 1.58824 x 10^-28 kg

binding energy = (change in mass (kg)) * (speed of light)²

binding energy = (1.58824 x 10^-28 kg) * (3 x 10⁸ m/s)²

binding energy = 1.43 x 10^-11 kg m² s^-2

binding energy = 1.43 x 10^-11 kg m² s^-2 * (1 J / 1 kg m² s^-2)

binding energy = 1.43 x 10^-11 J