0.37 mg Pb-206 0.95 mg U-238 4.5×10^9 yr

A rock contains 0.37 mg of Pb-206 and 0.95 mg of U-238.

The half-life of the decay series

U-238 → Pb-206 is 4.5×10^9 yr.

Assuming no Pb-206 was present in the rock initially,

how old is the rock?

[참고] 1차 반응. 방사성 붕괴는 1차 반응

N_t = 0.95 mg

N_0 = 0.95 mg U + 0.37 mg Pb × [(238 g/mol U) / (206 g/mol Pb)]

= 0.95 + 0.37 × [(238) / (206)]

= 1.3775 mg

반감기, t_1/2 = 0.693 / k

k = 0.693 / (4.5×10^9 yr)

= 1.54×10^(-10) /yr

ln(N_t / N_0) = –kt

t = –ln(N_t / N_0) / k

= –ln(0.95 / 1.3775) / (1.54×10^(-10))

= 2.41×10^9 yr

답: 2.4×10^9 yr

[키워드] U-238 방사성 붕괴 기준