The energy produced by converting 1 gram mass of a nuclear fuel into energy completely is:(a) 9 × 10¹⁶ J (b) 9 × 10¹⁴ J (c) 9 × 10¹⁵ J (d) 9 × 10¹³ J

(d) 9 × 1013 J

Explanation

Given, 

Mass, m = 1 gram = $\frac{1}{100}kg$           [converted gram into kilogram]

Speed of light, c = 3 × 10 ⁸m/s

Energy, E = ?

Solution

The energy produced by converting 1 gram $(\frac{1}{100}kg)$ mass of a nuclear fuel is given by Einstein's equation as:

$E=m{c}^{2}$

Substituting the given values in the above equation

$E=\left(\frac{1}{1000}\right)\times {\left(3\times {10}^{8}\right)}^{2}=9\times {10}^{13}J$