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QAIPM-2012-Ph-1677: NEET 2012 Physics - Class 12 AIPM-2012-Ph-1677 Solution: The half life of a radioactive nucleus is 50 days. The time…
The half life of a radioactive nucleus is 50 days. The time interval () between the time when of it has decayed and the time when of it had decayed is 30 days 50 days 60 days 15 days
Multiple Choice Options
- A 30 days
- B 50 days
- C 60 days
- D 15 days
Step-by-Step Verified Solution
At time t 2 , 2 3 of the sample had decayed
_ N = 1 3 N 0
_ 1 3 N 0 = N 0 e _ _ t 2 ......(1)
At time t 1 , 1 3 of the sample had decayed
_ N = 2 3 N 0
_ 2 3 N 0 = N 0 e _ _ t 1 ......(2)
Divide (i) by (ii), we get
1 2 = e _ _ t 2 e _ _ t 1
_ 1 2 = e _ _ ( t 2 _ t 1 )
_ _ ( t 2 _ t 1 ) = ln 2
_ ( t 2 _ t 1 ) = ln _ 2 _ = ln _ 2 ln _ 2 T 1 / 2 = T 1/2 = 50 days