After having a friend double check your calculations you realize that you would

Question

After having a friend double check your calculations you realize that you would feel much safer if you kept 1kg of Uranium-235 around the house– just in case the burglar brings a friend or two. However, you also realize that your physics teacher told you about radioactive decay. Any decay is associated with energy (heat) dissipation. So, you ask yourself how much heat your sample of 1kg Uranium-235 will release in 100years– after all you want children and grandchildren and they should also be safe at your house? You recall that the half-life time of 235 92 U is T1/2 = 2.1 · 1017years and each decay releases 200MeV.

Explanation / Answer

Atomic mass of Uranium-235 is 235.043924u

So 235.043924g of U-235 contains 1 mole of U-235 atoms or 6.022X1023atoms

So numebr of U-235 atoms is 1kg sample is N = [(6.022X1023)/(235.043924g)](1000g) = 25.62X1023

So, the sample has N = 25.62X1023atoms

Now t1/2 = ln2/, where t1/2 is half-life, and is decy constant.

So = ln2/t1/2 ------------- (1)

Activity is A = N

or A = (ln2/t1/2)N

So total number of decays in 100 years is;

Ndecay = (100year)[ln2/(2.1X1017year)]N = (100year)[0.693/(2.1X1017year)](25.62X1023)

or, Ndecay = 845.46X106

One decay releases energy = 200MeV

So heat energy released in 100 years is;

E = Ndecay(200MeV) =(845.46X106)(200MeV) = 1.69X1011MeV.

P.S.- the given value of half-life of U-235 is quite large compared to standard value. But I have used the given value...

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