4. (3) if a nuclear reaction produces 1.75 gigajoules of energy, what was the mass - defect in milligrams?

Explanation:

Step1: Recall Einstein's mass - energy equivalence formula

$E = mc^{2}$, where $E$ is energy, $m$ is mass, and $c = 3\times10^{8}\ m/s$. We need to solve for $m$, so $m=\frac{E}{c^{2}}$.

Step2: Convert the energy to SI units

Given $E = 1.75\ GJ=1.75\times 10^{9}\ J$.

Step3: Calculate the mass

$m=\frac{1.75\times 10^{9}\ J}{(3\times 10^{8}\ m/s)^{2}}=\frac{1.75\times 10^{9}}{9\times 10^{16}}\ kg$. $m=\frac{1.75}{9}\times10^{-7}\ kg$.

Step4: Convert the mass to milligrams

Since $1\ kg = 10^{6}\ mg$, then $m=\frac{1.75}{9}\times10^{-7}\times10^{6}\ mg=\frac{1.75}{9}\times10^{- 1}\ mg\approx0.0194\ mg$.

Answer:

$0.0194\ mg$