Answer : The time passed in years is 
Explanation :
Half-life = 5730 years
First we have to calculate the rate constant, we use the formula :



Now we have to calculate the time passed.
Expression for rate law for first order kinetics is given by:

where,
k = rate constant = 
t = time passed by the sample = ?
a = let initial amount of the reactant = X g
a - x = amount left after decay process = 
Now put all the given values in above equation, we get


Therefore, the time passed in years is 
TMS stands for Tetramethylsilane
Formula : Si(CH₃)₄
It is used as internal standard for chemical shift
In TMS all the four methyl groups are similar thus all the 12 hydrogen are chemically equivalent. They will show proton NMR at same level and which will appear as a singlet.
We have defined this singlet to be as reference set as zero.
Generally the other organic compounds show chemical shift downfield.So have positive chemical shift with respect to TMS shift.