Question #e70bd

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Question #e70bd

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Answer 1 · 2017-09-11T05:46:18

This is what I get for parts (i) to (iii)

Explanation:

Nuclear decay formula using half-life is

$N_t=N_0 xx2^((-t)/T_(1//2))$ ......(1)
where $N_t$ is sample of radioactive material remaining after time $t$ , $N_0$ is initial amount of sample and $T_(1//2)$ is half life of the sample.

The formula can also be written as

$N_t=N_0 xxe^((-0.693t)/T_(1//2))$ ......(2)

(i) Using equation (1)

$10^5=N_0 xx2^((-32)/2)$
$=>N_0 =10^5/2^((-32)/2)$
$=>N_0 =10^5xx2^16$
$=>N_0 =6.5536xx10^9$

(ii) Time $t$ when remaining sample A is equal to sample B can be calculated as the time when remaining sample $N_t=N_0/2$ , and sample B $=N_0/2$ .

We know that half-life for a given radioactive sample is the time for half the radioactive nuclei in that sample undergo radioactive decay.

$:.t=T_(1//2)=2s$

(iii) Inserting result of part (i) and given values in equation (1) we get

$N_t=(6.5536xx10^9)xx2^((-4096)/2)$
$N_t=390.625$
$N_t=390$ , rounded to previous lower integer. (as fraction of nucleus can not decay.

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