Thank you for posting your math problem here. To convert 3.9x10^5mg to dg the answer is <span>3.9 x 10^3 dg. Below is the solution:
Solution:
</span><span>1mg=0.01dg
</span><span> dg= 3.9 X 10^5mg
</span>dg = <span>(3.9 X 10^5) x 0.01
dg = </span><span>3.9 x 10^3 </span>
Radio active decay reactions follow first order rate kinetics.
a) The half life and decay constant for radio active decay reactions are related by the equation:



Where k is the decay constant
b) Finding out the decay constant for the decay of C-14 isotope:



c) Finding the age of the sample :
35 % of the radiocarbon is present currently.
The first order rate equation is,
![[A] = [A_{0}]e^{-kt}](https://tex.z-dn.net/?f=%20%5BA%5D%20%3D%20%5BA_%7B0%7D%5De%5E%7B-kt%7D%20%20%20)
![\frac{[A]}{[A_{0}]} = e^{-kt}](https://tex.z-dn.net/?f=%20%5Cfrac%7B%5BA%5D%7D%7B%5BA_%7B0%7D%5D%7D%20%3D%20e%5E%7B-kt%7D%20%20)


t = 7923 years
Therefore, age of the sample is 7923 years.
11.0 kg = (11.0 kg)(1000 g/kg) = 11000 g
(11000 g)/(1400 cm3) = 7.857 g/cm3
Simplified = 7.86 g/cm3
The percentage by mass of the compound of water is going to be 8.62%.