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Law of Radioactivity

The decay con...

Question

The decay constant of a radio isotope is $λ$ . If $A_{1}$ and $A_{2}$ are its activities at times $t_{1}$ and $t_{2}$ respectively, the number of nuclei which have decayed during the time $(t_{1} - t_{2})$

A_{1} t_{1} - A_{2} t_{2}

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A_{1} - A_{2}

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(A_{1} - A_{2}) / λ

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λ (A_{1} - A_{2})

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Solution

The correct option is C $(A_{1} - A_{2}) / λ$
$A_{1} = λ N_{1}$ at time $t_{1}$
$A_{2} = λ N_{2}$ at time $t_{2}$
Therefore, number of nuclei decayed during time interval $(t_{1} - t_{2})$ is
$N_{1} - N_{2} = \frac{[A_{1} - A_{2}]}{λ}$

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The decay constant of a radio isotope is λ. If A1 and A2 are its activities at times t1 and t2 respectively, the number of nuclei which have decayed during the time (t1−t2)

The correct option is C (A1−A2)/λA1=λN1 at time t1A2=λN2 at time t2Therefore, number of nuclei decayed during time interval (t1−t2) isN1−N2=[A1−A2]λ

The decay constant of a radio isotope is $λ$ . If $A_{1}$ and $A_{2}$ are its activities at times $t_{1}$ and $t_{2}$ respectively, the number of nuclei which have decayed during the time $(t_{1} - t_{2})$

The correct option is C $(A_{1} - A_{2}) / λ$
$A_{1} = λ N_{1}$ at time $t_{1}$
$A_{2} = λ N_{2}$ at time $t_{2}$
Therefore, number of nuclei decayed during time interval $(t_{1} - t_{2})$ is
$N_{1} - N_{2} = \frac{[A_{1} - A_{2}]}{λ}$