Question

Which of the following relation is dimensionally incorrect?

• A. 1 u = 931.5 MeV
• B. 1 u = 931.5 MeV/c${}^2$
• C. 1 u = 1.67 x 10${}^{-27}$kg
• D. None of these

Answer 1

Answer: (A)

1 u = 931.5 MeV

As, we know, $E=m{c}^2$
and energy released can be given as:
$E=931MeV$
for, $m=1u$

$1u=931.5MeV/c^2$ - Dimensionally correct [Dimension of mass]
$1u=1.67\times {10}^{-27}kg$ - Dimensionally correct [Dimension of mass]
but, $931.5MeV$ is having the dimension of energy so it can't be equated to dimension of mass or dimension of $1u$.
Hence, dimensionally correct data is given in $option\left(A\right)$
Hence, the correct option will be $\left(A\right)$