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Question : 30
Total: 37
(a) Define the term decay constant of a radioactive substance.
(b) The half-life of92 238 U 4.5 × 10 9 10 g 92 238 U
(b) The half-life of
Solution:
(a) Decay constant: Let the number of nuclei of a radioactive substance present at any time be N ( ∆ N ) ( ∆ t ) N ∆ t
∆ N ∝ N ∆ t
Or, ∆ N = − λ N ∆ t
The proportionality constantλ
(b) Half-life= 4.5 × 10 9
Mass number= 238
λ =
=
per year
N =
Hence, the activity,A = λ N
Or, A =
×
∴ A = 0.0039 × 10 15 = 3.9 × 10 12 per year
The proportionality constant
(b) Half-life
Mass number
Hence, the activity,
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