00:01
Hello students hope you are doing great.
00:04
So here we have to calculate the age of paper scroll and we are given the half life has 5 ,730 years and we are given the concentration of carbon 14 that is 0 .743 times that of the initial concentration.
00:20
So to calculate the age of paper scroll we will first calculate the value of k and we will be using the formula bt is equals to b0, t -res to the power kd where pd is amount after time that is equals to t and this is the initial amount.
00:57
T is time and the k is rate constant here.
01:00
To calculate the value of two, we are here asked to calculate the age of paper scroll and to calculate that we will first calculate the rate constant.
01:10
So we have t half is equals to 5, 7, 3 ,0 years.
01:24
Since it is p half, so we will have the final concentration as 0 .5 if we have the initial concentration as 1.
01:33
So we have pt is equals to p0 e -res to the power kt, putting the values 0 .5 is equals to p .0 is equal to p .1 into e -res -to -the -a -t.
01:45
The power k 5730 let us take natural log both the sides so it will be ln 0 .5 is equals to l n e k e r s to the power k into 5 730 now l n 0 .5 is equal to this k to 53730 will come here in the multiplication so it will be like k 55730 3 0 into lne.
02:24
We know that lne is equal to 1.
02:26
So we will calculate k as ln 0 .5 upon 5730.
02:36
That is equals to minus 0 .691 divided by 5730.
02:45
So we have the value of k as minus 0 .000000...