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Nuclei
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First Order Radioactive Decay
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Initial mass of a radioactive substance
Question
Initial mass of a radioactive substance is 3.2 mg. It has a half-life of 4 h. Find the mass of the substance left undecayed after 8 h.
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Updated on : 2022-09-05
Solution
Verified by Toppr
Given data :-
Initial Mass
=
M
0
=
3
.
2
m
g
t
1
/
2
=
4
m
To calculate , mass of the substance left undecayed after
8
h
[
M
z
=
8
]
we know,
M
(
z
)
=
M
0
e
−
λ
t
2
M
0
=
M
0
e
−
λ
(
4
)
⇒
λ
=
4
1
ln
(
2
)
M
(
8
)
=
M
0
.
e
−
λ
.
8
⇒
M
(
8
)
=
M
0
.
e
−
4
1
.
l
n
(
2
)
.
8
M
(
8
)
=
M
0
e
−
2
l
n
(
2
)
M
=
(
4
M
0
)
=
4
3
.
2
m
g
M
(
8
)
=
0
.
8
m
g
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