One of the first atomic explosion released approximately $1.0 \times 10 ^ { 14 } \mathrm {~J}$ of energy. How much matter had to be changed into energy to produce this yield? $\left( c = 3.0 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } \right)$
A) $23 \mathrm {~g}$
B) $13 \mathrm {~g}$
C) $1.1 \mathrm {~g}$
D) $0.45 \mathrm {~kg}$
E) $1.1 \mathrm {~kg}$

Question

Quizplus · Accepted Answer

To find the mass of matter converted into energy, use Einstein's equation $E = mc^2$. Rearranging for $m$, we get $m = \frac{E}{c^2}$. Substituting $E = 1.0 \times 10^{14} \, \text{J}$ and $c = 3.0 \times 10^8 \, \text{m/s}$, we find $m = \frac{1.0 \times 10^{14}}{(3.0 \times 10^8)^2} \approx 1.1 \, \text{g}$.

One of the First Atomic Explosion Released Approximately 1.0×1014 J1.0 \times 10 ^ { 14 } \mathrm {~J}1.0×1014 J

One of the First Atomic Explosion Released Approximately $1.0 \times 10 ^ { 14 } \mathrm {~J}$