Question

Half life of a radioactive sample is 4 days. After 16 days how much quantity of matter remain undecayed :

Answer 1

Concept Introduction: Half Life is generally calculated for Radioactive Substances.

Given:

We have been Given: Half Life of the substance is

$4 \: days$

To Find:

We have to Find: After

$16 \: days$

how much quantity of matter remain undecayed?

Solution:

According to the problem, therefore, Let the Original quantity be a0, and the decayed quantity be a. Therefore,

$n = \frac{ time}{half \: life \: time} = \frac{16}{4} = 4 \: days$

therefore by Rutherford-Soddy Formula,

$n = n_{0} { (\frac{1}{2}) }^{4} = \frac{ n_{0} }{16}$

therefore remaining quantity is,

$n_{0} - \frac{ n_{0} }{16} = \frac{16n_{0} - n_{0} }{16} = \frac{15n_{0} }{16}$

Final Answer: The remaining quantity is,

$\frac{15n_{0} }{16}$

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