300 g of an unknown radioactive substance decays to 112 g after 180 seconds. What is the half life of this substance ?
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Answered by
0
Answer:
2.1
minutes
Explanation:
The half-life equation states that,
A
=
A
0
⋅
(
1
2
)
t
t
0.5
A
0
is the initial amount of substance
t
is the time
t
0.5
is the half-life of the substance
We got:
A
0
=
300
g
,
A
=
112
g
,
t
=
180
s
=
3
min
.
And so,
112
g
=
300
g
⋅
(
1
2
)
3
min
t
0.5
(
1
2
)
3
min
t
0.5
=
112
g
300
g
=
0.37
ln
[
(
1
2
)
3
min
t
0.5
]
=
ln
0.37
3
min
t
0.5
⋅
ln
(
1
2
)
=
ln
0.37
3
min
t
0.5
=
ln
0.37
ln
(
1
2
)
t
0.5
3
min
=
ln
(
1
2
)
ln
0.37
t
0.5
=
3
min
⋅
ln
(
1
2
)
ln
0.37
≈
0.7
⋅
3
min
=
2.1
min
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