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

Step-by-step 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.

`(1000 g)/(270 g/mol) * 6.023 * 10^(23)atoms`

=
`2.229 * 10^(24)`

Hence, number of
`^(235)U` =
`(3)/(100) * 2.229 * 10^(24)`

=
`6.69 * 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 * 10^(22) * 200 * 10^(6) * 1.6 * 10^(-19)`

x =
`21.4 * 10^(9)` sec

Converting this value of x into years as follows.

x =
`(21.4 * 10^(9))/(3600 * 24 * 365)`

x =
`6.8 * 10^(2)` years

Thus, we can conclude that fissioning of the uranium in given situation requires
`6.8 * 10^(2)` years to keep a 100 W lamp burning.