The half life of a radioactive substance is 20 minutes . The approximate time interval (t_2 - t_1) between the time t_2 when 2/3 of it has decayed and - Physics MCQ FIITJEE AIEEE 2011 (Set Q) 2026 | ExamTest.live

mediumMCQFIITJEE AIEEE 2011 (Set Q)2026Physics

1 mark

The half life of a radioactive substance is 20 minutes . The approximate time interval (t_{2} - t_{1}) between the time t_{2} when \frac{2}{3} of it has decayed and time t_{1} when \frac{1}{3} of it had decayed is:

Solution & Step-by-step Explanation

Amount remaining at t_{1} is N_{1} = N_{0} (1 - 1/3) = \frac{2}{3} N_{0} .Amount remaining at t_{2} is N_{2} = N_{0} (1 - 2/3) = \frac{1}{3} N_{0} .Using N = N_{0} e^{- λ t} : \frac{N _{1}}{N _{2}} = \frac{2/3 N _{0}}{1/3 N _{0}} = 2 ⟹ e^{λ (t_{2} - t_{1})} = 2 λ (t_{2} - t_{1}) = ln 2 t_{2} - t_{1} = \frac{ln 2}{λ} Since T_{1/2} = \frac{l n 2}{λ} = 20 min, the time interval is 20 min .

Try it yourself before checking the explanation above.

The half life of a radioactive substance is 20 minutes . The approximate time interval (t_{2} - t_{1}) between the time t_{2} when \frac{2}{3} of it has decayed and time t_{1} when \frac{1}{3} of it had decayed is:

14 min

20 min

28 min

7 min

Practice with timed mock tests and track your performance across Physics.