Just #30 a rock contains 0.102 mg of lead-206 for each milligram of uranium-238. the half-life for decay of uranium-238 to lead-206 is 4.5 x 10^9 yr. the rock was formed yr ago.

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7.23 x 10^8 yr

Explanation: -

According to the question

The half life of uranium t ½ = 4.5 x 10^9 yr

Disintegration constant k =0.693 / t ½

= 0.693 / 4.5 x 10^9 yr

= 0.154 x 10^-9 yr

Let us assume there is 1 mg of Uranium present currently

Current uranium C = 1 mg

Original Uranium present O = Currently present + Transformed into lead

= 1 mg + (238 / 206) x 0.102 mg

= 1 + 0.118

=1.118 mg

Time taken =(1 / k) ln ( O/ C)

= (1 / 0.154 x 10^-9 yr) ln (1.118mg / 1 mg)

= 7.23 x 10^8 yr