Respuesta :
Explanation:
Molecular mass of [tex]UO_{2}[/tex] is the sum of molecular mass of U and [tex]O_{2}[/tex] molecule.
Molar mass of [tex]UO_{2}[/tex] = (238 + 32) g/mol
= 270 g/mol
Hence, in 1 kg there are 1000 grams. So, total number of atoms given molecules present in 1 kg will be calculated as follows.
[tex]\frac{1000 g}{270 g/mol} \times 6.023 \times 10^{23}atoms[/tex]
= [tex]2.229 \times 10^{24}[/tex]
Hence, number of [tex]^{235}U[/tex] = [tex]\frac{3}{100} \times 2.229 \times 10^{24}[/tex]
= [tex]6.69 \times 10^{22}[/tex]
Now, let x seconds is required for burning 100 W lamp bulb. As 200 MeV is released per reaction.
100 x = [tex]6.69 \times 10^{22} \times 200 \times 10^{6} \times 1.6 \times 10^{-19}[/tex]
x = [tex]21.4 \times 10^{9}[/tex] sec
Converting this value of x into years as follows.
x = [tex]\frac{21.4 \times 10^{9}}{3600 \times 24 \times 365}[/tex]
x = [tex]6.8 \times 10^{2}[/tex] years
Thus, we can conclude that fissioning of the uranium in given situation requires [tex]6.8 \times 10^{2}[/tex] years to keep a 100 W lamp burning.
