The activity of a radioactive substance is $R_{1}$ at time $t_{1}$ and $R_{2}$ at time $t_{2}$ where $t_{2} > t_{1}$ .Its decay constant is $λ$ .Then the number of atoms decayed between the time interval $t_{1}$ and $t_{2}$ are
$\frac{l n (2)}{λ} (R_{1} R_{2})$
$R_{1} e^{- λ t_{2}} - R_{2} e^{- λ t_{2}}$
$(\frac{R_{1} - R_{2}}{λ})$
$λ (R_{1} - R_{2})$

Question

The activity of a radioactive substance is $R_{1}$ at time $t_{1}$ and $R_{2}$ at time $t_{2}$ where $t_{2} > t_{1}$ .Its decay constant is $λ$ .Then the number of atoms decayed between the time interval $t_{1}$ and $t_{2}$ are
$\frac{l n (2)}{λ} (R_{1} R_{2})$
$R_{1} e^{- λ t_{2}} - R_{2} e^{- λ t_{2}}$
$(\frac{R_{1} - R_{2}}{λ})$
$λ (R_{1} - R_{2})$

Toppr Admin · Accepted Answer

B-apos-Let N1 be the number of atoms at t1-x2234-R1-x3BB-N1Let N2 be the number of atoms at t2-x2234-R2-x3BB-N2-x21D2-R1-x2212-R2-x3BB-N1-x2212-x3BB-N2-x21D2-N1-x2212-N2-R1-x2212-R2-x3BB-x2234-xA0- number of atoms decayed between the time interval t1 and t2 are R1-x2212-R2-x3BB-apos-

The activity of a radioactive substance is R1 at time t1 and R2 at time t2 where t2>t1.Its decay constant is λ.Then the number of atoms decayed between the time interval t1 and t2 areln(2)λ(R1R2)R1e−λt2−R2e−λt2(R1−R2λ)λ(R1−R2)

b'Let N1 be the number of atoms at t1∴R1=λN1Let N2 be the number of atoms at t2∴R2=λN2⇒R1−R2=λN1−λN2⇒N1−N2=R1−R2λ∴ number of atoms decayed between the time interval t1 and t2 are R1−R2λ'