Question

In a sample of UO 2, the uranium has been enriched so that 3.0% of it is 235U. How long could the fissioning of the uranium in this 1.0 kg sample keep a 100 W lamp burning?

Answer 1

Explanation:

Molecular mass of $UO_{2}$ is the sum of molecular mass of U and $O_{2}$ molecule.

             Molar mass of $UO_{2}$ = (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.

          $\frac{1000 g}{270 g/mol} \times 6.023 \times 10^{23}atoms$

                     = $2.229 \times 10^{24}$

Hence, number of $^{235}U$ = $\frac{3}{100} \times 2.229 \times 10^{24}$

                                            = $6.69 \times 10^{22}$

Now, let x seconds is required for burning 100 W lamp bulb. As 200 MeV is released per reaction.

             100 x =  $6.69 \times 10^{22} \times 200 \times 10^{6} \times 1.6 \times 10^{-19}$

                    x = $21.4 \times 10^{9}$ sec

Converting this value of x into years as follows.

                       x = $\frac{21.4 \times 10^{9}}{3600 \times 24 \times 365}$

                    x = $6.8 \times 10^{2}$ years

Thus, we can conclude that fissioning of the uranium in given situation requires $6.8 \times 10^{2}$ years to keep a 100 W lamp burning.