Two radioactive samples X and Y having half life 3 years and 2 years respectively have been decaying for many years. Today both samples have equal number of atoms. The number of atoms in the sample X

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Two radioactive samples X and Y having half life 3 years and 2 years respectively have been decaying for many years. Today both samples have equal number of atoms. The number of atoms in the sample X will be twice of the number of atoms in the sample Y after

TestHub · Accepted Answer

​ N 0 ​ e − λ t = 2 ( N 0 ​ e − λ 2 ​ t ) ⇒ e − λ 1 ​ t = 2 e − λ 2 ​ t ⇒ e − ( λ 1 ​ − λ 2 ​ ) t = 2 ⇒ ( λ 2 ​ − λ 1 ​ ) t = ln 2 ​ ⇒ ( t 2 ​ ln 2 ​ − t 1 ​ ln 2 ​ ) t = ln 2 ⇒ t = ( t 1 ​ − t 2 ​ t 1 ​ t 2 ​ ​ ) = 6 years. ] ​

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