Question

1. what is the amount of energy released in the nuclear - reaction of 95 kilograms of uranium? multiple - choice options not clearly visible 2. how much mass is required to create a nuclear explosion that will release 3.40×10^18 joules of energy? multiple - choice options not clearly visible 3. the isotope lawrencium - 262 has a half - life of 4 hours. if a sample has an initial mass of 1024 grams, then how much of the sample will remain after 20 hours. multiple - choice options not clearly visible

Explanation:

Step1: Identify relevant physics formula

For energy - mass relation, use $E = mc^{2}$, for half - life use $m = m_0(\frac{1}{2})^{\frac{t}{T_{1/2}}}$.

Step2: Solve first question

$E=mc^{2}$, with $m = 95\ kg$ and $c = 3\times10^{8}\ m/s$, $E=95\times(3\times 10^{8})^{2}=8.55\times10^{19}\ J$.

Step3: Solve second question

From $E = mc^{2}$, $m=\frac{E}{c^{2}}$, with $E = 3.40\times10^{18}\ J$, $m=\frac{3.40\times10^{18}}{(3\times10^{8})^{2}}\approx 0.0378\ kg = 37.8\ g\approx40\ g$.

Step4: Solve third question

$T_{1/2}=4\ h$, $t = 20\ h$, $n=\frac{t}{T_{1/2}} = 5$, $m = m_0(\frac{1}{2})^{n}$, $m_0 = 192\ g$, $m=192\times(\frac{1}{2})^{5}=6\ g$.

Answer:

First question: No options match calculated value.
Second question: 40 g (approximate match to option).
Third question: 6 g (no option shown but calculated value).