Age of wood and fossil source : newatlas.com

## To calculate the age of wood and fossil or bone-

The age of  wood and fossil or bone is determined by Carbon dating method. Activity of  C 14 is determined in the leaving plant or animal and then activity of C14 is determined in old wood or fossil. the following formula is used to determine the age of dead animal or plant-

#### K = (2.303 / t) [log  ( N0 / N )]

Number of atoms of C14 or gram atoms of C14 may be taken in place of activity.

## Numerical-

### Solution )

#### K = (2.303 /t [log)  ( activity of C14 in fresh wood or animal / activity of C14 in dead wood or animal )

activity of C14 in fresh wood = 14 particles

activity of C14 in old  wood = 7 particles

Age of wood ( t) = ?

t1/2 = 5770 years

K = 0.693 / t1/2 = 0.693/ 5770 = 0.00012= 1.2 x 10-4 years -1

K = 2.303 / t [ log 14 / 7 ]

1.2 x 10 -4 =( 2.303 / t )[ log 2]

t = (2.303 / 1.2 x 10-4 )[0.3010 ] = 2.303 x 0.3010 / 1.2 x 10-4

### Solution )

Mass of C14 in living plant / Mass of C14 in wood piece remain  = 16 / 1

Means N=1, N0 = 16

t1/2 = 5577 years

K = 0.693 / t1/2 = 0.693/ 5577 = 0.000124 = 1.24 x 10-4 years-1

#### K = 2.303 /t [log  ( N0 / N )]

t  = 2.303 / K  [ log 16 / 1]

t  = 2.303 / K  [ log 24 ]

t = (2.303 / 1.24 x 10-4 )[4 log 2 ]

t = (2.303 / 1.24 x 10-4 )[4 x 0.3010 ] = 2.303 x 0.3010 x 4 / 1.24 x 10-4

### Solution )

t1/2 =  28.1 years , initial amount ‘N0‘ = one microgram = 10-6 gm , N =? , t = 20 years

K = 0.693 / t 1/2 = 0.693/ 28.1 = 0.0246  years-1

#### K = 2.303 /t [log  ( N0 / N )]

0.0246 = (2.303 / 20)[log 10-6 / N]

0.0246 x 20 / 2.303 = log 10-6 / N

0.2136 = log 10-6 / N

log 10-6 / N =Antilog 0.2136 = 1.635

N = 10-6 / 1.635 = 0.611 x 10-6

### Solution )

t1/2 = 5760 years , N0 = 1 gm , N = 0.25 gm , t =?

K = 0.693 / t1/2 = 0.693/ 5760 = 0.00012 = 1.2 x 10-4 years-1

#### K = (2.303 /t) [log  ( N0 / N )]

t  = 2.303 / K  [ log 1 /0.25]

= 2.303 / K  [ log 4]

t= 2.303 / K  [ log 22 ]

= (2.303 / 1.2 x 10-4 )[2 log 2 ]

t = (2.303 / 1.2 x 10-4 )[2 x 0.3010 ] = 2.303 x 0.3010 x 2 / 1.2  x 10-4