Question

Which of the following relations is dimensionally incorrect?

(A) 1 a.m.u =931.5MeV. (B). 1 a.m.u = 931.5MeV/c²
(C) 1 a.m.u = 1.67×10^-27Kg. (D). None of these

Answer 1

Energy equivalent of 1 u is given by: E=mc2=1.67×10-27×3×1082=15.03×10-11 J=15.03×10-111.6×10-13 MeV= 939 MeV according to the data given this will be an exact answer. Now about dimensional analysis. Obviously, mass dimension is not equal to energy dimension. But by 1 u=939 MeV what actually meant is the energy equivalence of 1 u mass. Writing it like this is not wrong, it is used all the time but in nuclear and particle physics only. One example is Higgs boson. When CERN announced its mass, they didn't say the mass is kg or u, they said 125 GeV. This actually means the mass of the boson is 125 GeV/c2.

therefore option (d) is the answer