# How many of the nuclei of a radioactive sample containing 2048 nuclei decay in 3 years, if it's half life is given to be 6 months ?

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How many of the nuclei of a radioactive sample containing 2048 nuclei decay in 3 years, if it's half life is given to be 6 months ?

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Step 1

Half life of a radioactive sample is the time in which half of the sample is decayed i.e. 50% of the radioactive sample remains.

Radioactive decay follows first order kinetcsand hence, half life is independent of the initial concentration.

Step 2

Half life of given sample is 6 months

It means after every 6 months, the radioactive nuclei present in the sample will be reduced to half.

Number of radioactive nuclei present intially = 2048

After 6 months (one half life) , radioactive nuclei remaining = 2048/2 = 1024

After 1 years (two half lives), radioactive nuclei remaining = 1024/2 = 512

After 1 year and 6 months (three half lives), radioactive nuclei remaining = 512/2 = 256

After 2 years (four half lives), radioactive nuclei remaining = 256/2 = 128

After 2 years and 6 months (five half lives), radioactive nuclei remaining = 128/2 = 64

After 3 years (six half lives), radioactive nuclei remaining = 64/2 = 32

Hence, nuclei decayed after 3 years = Initial nuclei - Nuclei remaining after 3 years = 2048 - 32 = 2016

Step 3

Alternative method:

A/Ao = (1/2)n

Here, A is Nuclei remaining after 'n' half lives

Ao is initial number of nuclei

'n' is number of half lives

Now, in 3 years, number of half lives = 6.

So, 'n' = 6

Ao = 2048

Substituting the values,

(A/2048) = ...

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