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""^(226)Ra disintegrates at such a rate ...

`""^(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

A

790 years

B

3160 years

C

1580 years

D

6230 years

Text Solution

Verified by Experts

The correct Answer is:
C
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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