Question
A radio-active material is reduced to 1 / 8 of its original amount in 3 days. If 8 10^ -3 ~kg of the material is left after 5 days. The initial amount of the material is
BITSAT
Physics
Nuclear Physics
2023
BITSAT 2023 (Memory Based Paper 1)
BITSAT Physics Question (2023) — Solution
Options
- A. 700 gm
- B. 900 gm
- C. 475 gm
- D. 256 gm
Answer
D. 256 gm
Step-by-step solution
N = N _0 ( 1 2 )^ n N = N _0 8 N _0 8 = N _0 ( 1 2 )^ n ( 1 2 )^3= ( 1 2 )^ n n =3 3 half lives =3 days 1 half life =1 day 5 days =5 half life N = N _0 ( 1 2 )^ n 8 10^ -3 = N _0 ( 1 2 )^5 N_0=2^5 8 10^ -3 =256 gm
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