Uranium ores contain one radium −226 atoms for every 2.8×106 uranium −238 atoms. Calculate the half - life of 23892U, given that the half - life of 22688Ra is 1600 years. (22688Ra is a decay product of 23892U)
A
1.75×103years
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B
1600×23892years
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C
4.55×109years
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D
1600years
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Solution
The correct option is C4.55×109years Activity of uranium atom and activity of radium is equal. ⇒λUNU=λRaNRa
or NUτU=NRaτRa
or NUln2τU=NRaln2τRa NUtU=NRatRa 2.8×106tU=11600 tU=4.5×109years