At time $t = 0, N_1$ nuclei of decay constant $\lambda _1 \,\& \,N_2$ nuclei of decay constant $\lambda _2$ are mixed . The decay rate of the mixture is :
At time $t = 0, N_1$ nuclei of decay constant $\lambda _1 \,\& \,N_2$ nuclei of decay constant $\lambda _2$ are mixed . The decay rate of the mixture is :
- A
${N_1}{N_2}{e^{ - \left( {{\lambda _1} + {\lambda _2}} \right)t}}$
- B
$ + \left( {\frac{{{N_1}}}{{{N_2}}}} \right){e^{ - \left( {{\lambda _1} - {\lambda _2}} \right)t}}$
- C
$ + ({N_1}{\lambda _1}{e^{ - {\lambda _1}t}} + {N_2}{\lambda _2}{e^{ - {\lambda _2}t}})$
- D
$ + {N_1}{\lambda _1}{N_2}{\lambda _2}{e^{ - \left( {{\lambda _1} + {\lambda _2}} \right)t}}$
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${N}_{{A}}(0)={No} . \text { of } {A} \text { atoms at } {t}=0$
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At time $t=0$, a material is composed of two radioactive atoms ${A}$ and ${B}$, where ${N}_{{A}}(0)=2 {N}_{{B}}(0)$ The decay constant of both kind of radioactive atoms is $\lambda$. However, A disintegrates to ${B}$ and ${B}$ disintegrates to ${C}$. Which of the following figures represents the evolution of ${N}_{{B}}({t}) / {N}_{{B}}(0)$ with respect to time $t$ ?
${N}_{{A}}(0)={No} . \text { of } {A} \text { atoms at } {t}=0$
${N}_{{B}}(0)={No} . \text { of } {B} \text { atoms at } {t}=0$
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