1.

.^(226)Ra disintegrates at such a rate that after 3160 years only one fourth of its original amount remains. The half-life of .^(226)Ra will be

Answer»

790 years
3160 years
1580 years
6230 years

Solution :For an element to disintegrate
`N = N_(0) ((1)/(2))^(n)...(i), t = n XX t_(1//2)` ...(ii)
For `RA^(226) (N)/(N_(0)) = (1)/(4)`, from eq. (i)
`(1)/(4) = ((1)/(2))^(n) or ((1)/(2))^(n) or ((1)/(2))^(2) = ((1)/(2))^(n) , n = 2`, from eq. (ii)
`T_(1//2) = (t)/(n) = (3160)/(2) = 1580 yrs`


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