A radioactive substance is known to decay at a
rate proportional to the amount present. If initially there is 100
milligrams of the radioactive substance present and after two
hours it is observed that the radioactive substance has lost 10
percent of its original mass, find the half life of the radioactive
substance.
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Answered by
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Answer:
i dont know hope you understand
Answered by
0
Step-by-step explanation:
let the amount of radioactive material be α
Given that,⟹−
dt
dα
=kα
Where k is the proportionality constant
⟹
α
1
dα=
k
−1
dt
let α
0
be the initial amount taken,
solving the differential equation gives,
α=α
0
e
−kt
Given that after an hour 10percent of the given material has been decayed,
substituting this in the obtained equation gives,
10
9α
0
=α
0
e
−k
Thus, we can obtain the value of k from this equation.
k=0.105379
Now for finding the half life,
2
α
0
=α
0
e
−tk
∴t
2
1
=
k
0.693
⟹t
2
1
=
0.105379
0.693
∴t
2
1
=6.58hrs
see this u may get an idea
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