1.

A sample of U - 238 (half-life = 4.5 xx 10^(9)yr) ore is found to contain 23.8 g of U-238 and 20.6 g of Pb - 206. What will be the age of theore?

Answer»

`5.5 XX 10^(12)` years
`6.0 xx 10^(8)` years
`4.5 xx 10^(9)` years
`5.5 xx 10^(14)` years

Solution :Disintegration occurs as :
`""_(92)U^(238) to ""_(82)Pb^(206) + 8 ""_(2)He^(4) + e ""_(-1)e^(0)`
ATOMS of Pb present = `(20.6)/(206) = 0.1 g ` atom = U DECAYED
Atoms of U present = `(23.8)/(238) = 0.1 g` atom
`:. N = 0.1 g` atom
`N_0` = U present + U decayed = `0.1 + 0.1 = 0.2 g` atom
`t = (2.303 xx 4.5 xx 10^(9))/(0.693) "LOG"_(10)(0.2)/(0.1)`
`:. t = 4.5 xx 10^(9) ` years.


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