Even though plutonium−239 (t1/2 = 2.41 × 104 yr) is one of the main fission fuels, it is still a radiation hazard present in spent uranium fuel from nuclear power plants. how many years does it take for 83% of the plutonium−239 in spent fuel to decay?

6.468*103 years

Explanation:

The half life refers to the time it takes for the radioactive sample to decay to half the initial amount present. The detailed solution is found in the image attached. The formula used here is used to brain the time taken for a given amount of radioactive material to decay if the half life and original amount of radioactive material in the sample is known.

the catch is that the top numbers are atomic masses the bottom numbers are the numbers of protons and electrons in an uncharged atom. they are the number of that atoms as you would find them on the periodic table. further, the numbers on the left are used to determine the missing numbers on the right

so here we go

atomic mass

239 + 1 = y + 134 + 3 combine like terms

240 = y + 137             subtract 137 from both terms

240 - 137 = y

103 = y

atomic number

94 = z +54 + 0

94 = z + 54               subtract 54 from both sides.

40 = z

answer

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