How to find diffence in atomic mass of two isotopes if binding energy is given?
Answers
You will need to use Albert Einsteins famous relativity equation E = mc^2, where E (also written as BE) is binding energy, m is the mass defect, and c is the speed of light (in this case it is squared). The mass defect is the difference between the sum of the mass of all the individual nucleons that make up the nucleus, and the nucleus itself. It is usually measured in atomic mass units, where 1 atomic mass unit is the mass of 1/12 of a carbon 12 atom. 1 atomic mass = 1.661*10^-27 kg. Multiplying the mass defect by the speed of light squared will give you binding energy.
For example, to find the binding energy of 1 atomic mass unit;
E = mc^2
E = (1.661*10^-27)*(3*10^8)^2
E = (1.661*10^-27)*(9*10^16)
E = 1.4949*10^-10 J
You will often be asked to convert binding energy from joules to electron volts (eV). 1 eV is the work done to move accelerate an electron across a potential difference of 1 volt. Work done= charge*potential difference and for 1 eV, potential difference is 1 volt so work done is simply the same as the charge on an electron, which is equal to 1.6*10^-19 C * 1V = 1.6*10^-19 J. The magnitude of the work is the same as the charge of the electron but the units are different because the charge was multiplied by the 1 volt to get the work done.
To convert the 1.4949*10^-10 J into eV, simply divide it buy the 1.6*10^-19 J that 1 eV takes. (1.4949*10^-10 J)/(1.6*10^-19 J) = 934312500 eV, which can be divided by one million to give 934.3 MeV.
Hope this answers the question.