What is the nuclear binding energy for thorium-234? 2.78 * 10-10 J 3.36 * 10-14 J 1.67 * 1017 J 5.35 x 10-23 J

The correct option is A.

To calculate the binding energy, you have to find the mass defect first.

Mass defect = [mass of proton and neutron] - Mass of the nucleus

The molar mass of thorium that we are given in the question is 234, the atomic number of thorium is 90, that means the number of neutrons in thorium is

234 - 90 = 144.

The of proton in thourium is 90, same as the atomic number.

Mass defect = {[90 * 1.00728] + [144 * 1.00867]} - 234

Note that each proton has a mass of 1.00728 amu and each neutron has the mass of 1.00867 amu.

Mass defect = [90.6552 + 145.24848] - 234 = 1.90368 amu.

Note that the unit of the mass is in amu, it has to be converted to kg

To calculate the mass in kg

Mass [kg] = 1.90368 * [1kg/6.02214 * 10^-26 = 3.161135 * 10^-27

To calculate the binding energy

E = MC^2

C = Speed of light constant = 2.9979245 * 10^8 m/s2

E = [3.161135 * 10^-27] * [2.9979245 * 10^8]^2

E = 2.84108682069 * 10^-10.

Note that we arrive at this answer because of the number of significant figures that we used.

So, from the option given, Option A is the nearest to the calculated value and is our answer for this problem.