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 ?
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.
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
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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