Question

a pure sample of a radioactive substance has 16*10^12 atoms
and the half life is 3 minutes. How long does it take until 5*10^11
atoms of the substance have not yet decayed?

Answer #1

**Given
**

** pure radio active substance initially N0 =
16*10^12 atoms are there**

** half life time T1/2 = 3 min = 180
s**

** **

**we know that T1/2 = 0.693/ Lambda LAmbda is decaay
constant**

** lambda = 0.693/180 = 0.00385 desintigrations
per sec**

** and the relation N = N0
e^(-Lambda*t)**

** **

**
5*10^11 = 16*10^12*e^(-0.00385*t)**

** t =
900.191 s
t = 15
min**

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Radioactive Half-life
Years
Element A Remaining Radioactive Atoms
Element B Remaining Radioactive Atoms
Element C Remaining Radioactive Atoms
Element D remaining Radioactive Atoms
0
100
100
100
100
1000
50
85
90
95
2000
25
72
81
90
3000
13
61
73
86
4000
6
52
66
81
5000
3
44
59
77
6000
2
38
53
74
7000
1
32
48
70
8000
0
27
43
66
9000
0
23
39
63
10000
0
20
35
60
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