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Question : 6
Total: 6
(a) Write the relation between half life and average life of a radioactive nucleus.
(b) In a given sample two isotopes,A 1 : 2 2 : 1
(b) In a given sample two isotopes,
Solution:
(a) Relation between average life and half life
(b) Finding the required time
(a)T =
Alternatively(
) ∕ (
) ∕ 1.44 T 1 ∕ 2
(b) We haveN = N 0 e − λ . t
=
,
=
∴
=
exp ( − ( λ 1 − λ 2 ) t )
∴ 2 =
exp ( − ( λ 1 − λ 2 ) t )
⇒ exp ( − ( λ 1 − λ 2 ) t ) = 4
⇒ − ( λ 1 − λ 2 ) t = 2 ln 2
⇒ − ln 2 (
−
) t = 2
⇒
= 2
⇒ t = 120 years
(b) Finding the required time
(a)
Alternatively
(b) We have
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