Age of earth or mineral source : Facebook

## Age of earth or mineral-

Uranium – Lead dating method is used to determine the age of earth or a mineral. One gram atom of U238 disintegrates to give one gram atom of Pb 206. Gram atoms of U238 and Pb 206 are determined in the given sample. To use the following formula , it is assumed that no lead was present originally in the mineral-

### Solution )

Half life of uranium (t1/2) = 4.5 x 109 years

K = 0.693 / t1/2 = 0.693 / 4.5 x 109

K = 0.154 x 10-9 = 1.54 x 10-10 years-1

Weight of uranium = 23.8 gm

Gram atoms of U 238 = w/m = 23.8 / 238 = 0.1

Gram atoms of Pb 206  =w/m = 20.6 / 206 = 0.1

### t = (2.303 / K) [log( gram atom of U 238 + gram atom of Pb 206 )/ gram atom of U 238 ]

= (2.303 / 1.54 x 10-10 ) [log (0.1 + 0.1)/ 0.1]

= 1.495 x 1010( log 2)

Because ,log 2 = 0.3010

= 1.495 x 1010 x 0.3010 = 0.4499 x 1010

### Solution )

Half life of uranium (t1/2) = 4.5 x 109 years

K = 0.693 / t1/2 = 0.693 / 4.5 x 109

K = 0.154 x 10-9 = 1.54 x 10-10 years-1

Weight of uranium = 1.0  gm

Gram atoms of U 238 = w/m = 1.0 / 238 = 0.0042

Gram atoms of Pb 206 =w/m = 0.1 / 206 = 0.000485

### t = (2.303 / K) [log( gram atom of U 238 + gram atom of Pb 206 )/ gram atom of U 238 ]

= (2.303 / 1.54 x 10-10 ) [log (0.0042 + 0.000485)/ 0.0042]

= 1.495 x 1010[log ( 0.004685)/ 0.0042]

= 1.495 x 1010( log 1.1154)

Because ,log 1.1154 = 0.0474

= 1.495 x 1010 x 0.0474 = 0.0708 x 1010

### Solution )

Let , age of earth = t years

Weight of uranium = 1.667  gm

Gram atoms of U 238 = w/m = 1.667 / 238 = 0.0070

Gram atoms of Pb 206 =w/m = 0.277 / 206 = 0.001345

half life of uranium (t1/2) = 4.51 x 109 years

K = 0.693 / t1/2 = 0.693 / 4.51 x 109

K = 0.154 x 10-9 = 1.54 x 10-10 years -1

### t = (2.303 / K) [log( gram atom of U 238 + gram atom of Pb 206 )/ gram atom of U 238 ]

= (2.303 / 1.54 x 10-10 ) [log (0.0070 + 0.001345)/ 0.0070]

= 1.495 x 1010 [log ( 0.00835)/ 0.0070]

= 1.495 x 1010( log 1.192)

Because , log 1.192 = 0.07658

t = 1.495 x 1010 x 0.07658 = 0.1144 x 1010