The radioactivity of a sample is R1 at a time T1 and R2 at times T2 . the half-life of the specimen is T, the number of atoms that have disintegrated at the time (T2-T1) is proportional to

Question

The radioactivity of a sample is R1 at a time T1 and R2 at times T2 . the half-life of the specimen is T, the number of atoms that have disintegrated at the time (T2-T1) is proportional to (A)  R1T1-R2T2  (B)  R1-R2  (C)  (R1-R2/T)  (D)  (R1-R2)T

Tardigrade Admin · Accepted Answer

R1=N1 λ and R2=N2 λ Also T=( log e 2/λ) Or λ=( log e 2/T) ∴ R1-R2=(N1-N2) λ =(N1-N2) ( log e 2/T) ∴ (N1-N2)=((R1-R2) T/ log e 2) ie, (N1-N2) propto(R1-R2) T

Q. The radioactivity of a sample is $R_{1}$ at a time $T_{1}$ and $R_{2}$ at times $T_{2}$ . the half-life of the specimen is $T$ , the number of atoms that have disintegrated at the time $(T_{2} - T_{1})$ is proportional to

$R_{1} T_{1} - R_{2} T_{2}$

$R_{1} - R_{2}$

$\frac{R _{1} - R _{2}}{T}$

$(R_{1} - R_{2}) T$

Q. The radioactivity of a sample is R1​ at a time T1​ and R2​ at times T2​ . the half-life of the specimen is T, the number of atoms that have disintegrated at the time (T2​−T1​) is proportional to

R1​T1​−R2​T2​

R1​−R2​

TR1​−R2​​

(R1​−R2​)T

R1​=N1​λ and R2​=N2​λ Also T=λloge​2​ Or λ=Tloge​2​ ∴R1​−R2​=(N1​−N2​)λ =(N1​−N2​)Tloge​2​ ∴(N1​−N2​)=loge​2(R1​−R2​)T​ ie, (N1​−N2​)∝(R1​−R2​)T

Q. The radioactivity of a sample is $R_{1}$ at a time $T_{1}$ and $R_{2}$ at times $T_{2}$ . the half-life of the specimen is $T$ , the number of atoms that have disintegrated at the time $(T_{2} - T_{1})$ is proportional to

$R_{1} T_{1} - R_{2} T_{2}$

$R_{1} - R_{2}$

$\frac{R _{1} - R _{2}}{T}$

$(R_{1} - R_{2}) T$