Question

The energy equivalent of $2.0\text{mg}$ mass defect is:

• A. $1.8\times {10}^4\text{erg}$
• B. $9\times {10}^{-19}\text{erg}$
• C. $1.5\times {10}^{20}\text{erg}$
• D. $1.8\times {10}^{18}\text{erg}$

Answer 1

The correct option is D $1.8\times {10}^{18}\text{erg}$

Using the relation, $\Delta \text{E}=\Delta \text{m}\times {\text{C}}^2(\Delta \text{m}$ in $\text{kg},\Delta \text{E}$ in $\text{J})$
$2\text{mg}=2\times {10}^{-6}\text{kg}$
$\therefore \Delta \text{E}=2\times {10}^{-6}\times (3\times {10}^8{)}^2\text{J}$
= $2\times {10}^{-6}\times 9\times {10}^{16}\text{J}=18\times {10}^{10}\text{J}$
= $18\times {10}^{10}\times {10}^7\text{erg}(1\text{J}={10}^7\text{erg})$
= $1.8\times {10}^{18}\text{erg}$