Answer:
15.625 g of a 500 gram sample of potassium-42 with 12.4 hours of Half -life is left after 62 hours.
The half-life is the time after which half of the initial quantity of a radioactive substance is left .
Given here,
The half-life of K-42 = 12.4 hours
The initial quantity of K-42 = 500 gm
The final quantity after 62 hours = ?
The number of half cycle
\bold { = 62\times \dfrac 1{12.4} = 5,}=62×
12.4
1
=5,
Thus the number of half life cycles in 62 hours is 5,
After 1 half life \bold {= \dfrac {500}{2} = 250}=
2
500
=250
After 2 half lives \bold {= \dfrac {250}{2} = 125}=
2
250
=125
After 3 half lives \bold {= \dfrac {125}{2} = 62.5}=
2
125
=62.5
After 4 half lives \begin{gathered}\bold {= \dfrac {62.5}{2} = 31.25}\\\end{gathered}
=
2
62.5
=31.25
After 5 half lives \begin{gathered}\bold {= \dfrac {31.25}{2} = 12.625}\\\end{gathered}
=
2
31.25
=12.625
15.625 g of a 500 gram sample of potassium-42 with 12.4 hours of Half -life is left after 62 hours.
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