a.) The two daughter nuclei have half the volume of the originaluranium nucleus, so their radii are smaller by a factor of \(\displaystyle\sqrt{{{3}}}{\left\lbrace{2}\right\rbrace}\)

\(\displaystyle{r}={\frac{{{7.4}\times{10}^{{-{15}}}}}{{\sqrt{{{3}}}{\left\lbrace{2}\right\rbrace}}}}={5.9}\times{10}^{{-{15}}}\) m

b) \(\displaystyle{U}={\frac{{{k}{\left({46}{e}\right)}^{{2}}}}{{{2}{r}}}}={\frac{{{k}{\left({46}\right)}^{{2}}{\left({1.6}\times{10}^{{-{19}}}\right)}^{{2}}}}{{{1.17}\times{10}^{{-{14}}}}}}={4.14}\times{10}^{{-{11}}}\) J

Each daughter has half of the potential energy turn into itskinetic energy when far from each other, so

\(\displaystyle{K}={\frac{{{U}}}{{{2}}}}={\frac{{{4.14}\times{10}^{{-{11}}}}}{{{2}}}}={2.07}\times{10}^{{-{11}}}\) J

c) If we have 10.0 kg of uranium, then the number of nucleiis

\(\displaystyle{n}={\frac{{{10}}}{{{236}{u}{\left({1.66}\times{10}^{{-{27}}}\right)}}}}={2.55}\times{10}^{{{25}}}\) nuclei

And each releases energy:

\(\displaystyle{E}={n}{U}={\left({2.55}\times{10}^{{{25}}}\right)}{\left({4.14}\times{10}^{{-{11}}}\right)}={1.06}\times{10}^{{{15}}}\) J

\(\displaystyle={253}\) kilotons of TNT

d.) We could call an atomic bomb an “electric” bomb sincethe electric potential energy provides the kinetic energy of the particles

\(\displaystyle{r}={\frac{{{7.4}\times{10}^{{-{15}}}}}{{\sqrt{{{3}}}{\left\lbrace{2}\right\rbrace}}}}={5.9}\times{10}^{{-{15}}}\) m

b) \(\displaystyle{U}={\frac{{{k}{\left({46}{e}\right)}^{{2}}}}{{{2}{r}}}}={\frac{{{k}{\left({46}\right)}^{{2}}{\left({1.6}\times{10}^{{-{19}}}\right)}^{{2}}}}{{{1.17}\times{10}^{{-{14}}}}}}={4.14}\times{10}^{{-{11}}}\) J

Each daughter has half of the potential energy turn into itskinetic energy when far from each other, so

\(\displaystyle{K}={\frac{{{U}}}{{{2}}}}={\frac{{{4.14}\times{10}^{{-{11}}}}}{{{2}}}}={2.07}\times{10}^{{-{11}}}\) J

c) If we have 10.0 kg of uranium, then the number of nucleiis

\(\displaystyle{n}={\frac{{{10}}}{{{236}{u}{\left({1.66}\times{10}^{{-{27}}}\right)}}}}={2.55}\times{10}^{{{25}}}\) nuclei

And each releases energy:

\(\displaystyle{E}={n}{U}={\left({2.55}\times{10}^{{{25}}}\right)}{\left({4.14}\times{10}^{{-{11}}}\right)}={1.06}\times{10}^{{{15}}}\) J

\(\displaystyle={253}\) kilotons of TNT

d.) We could call an atomic bomb an “electric” bomb sincethe electric potential energy provides the kinetic energy of the particles