Answer:
a)
fraction of carbon−14 in a piece of charcoal remains after 14.0 years.
b)
fraction of carbon−14 in a piece of charcoal remains after 
c)
fraction of carbon−14 in a piece of charcoal remains after
.
Explanation:
The fraction of a radioactive isotope remaining at time t is given by:
![[A]=\frac{(\frac{1}{2})^t}{t_{\frac{1}{2}}}](https://tex.z-dn.net/?f=%5BA%5D%3D%5Cfrac%7B%28%5Cfrac%7B1%7D%7B2%7D%29%5Et%7D%7Bt_%7B%5Cfrac%7B1%7D%7B2%7D%7D%7D)
Taking log both sides:
![\log [A]=t\log[\frac{1}{2}]-\log [t_{\frac{1}{2}}]](https://tex.z-dn.net/?f=%5Clog%20%5BA%5D%3Dt%5Clog%5B%5Cfrac%7B1%7D%7B2%7D%5D-%5Clog%20%5Bt_%7B%5Cfrac%7B1%7D%7B2%7D%7D%5D)
[A] = fraction at given time t
= half life of the carbon−14 =5,730 years
a)When , t = 14 years
![\log [A]=t\log[\frac{1}{2}]-\log [t_{\frac{1}{2}}]](https://tex.z-dn.net/?f=%5Clog%20%5BA%5D%3Dt%5Clog%5B%5Cfrac%7B1%7D%7B2%7D%5D-%5Clog%20%5Bt_%7B%5Cfrac%7B1%7D%7B2%7D%7D%5D)
![\log [A]= 14 years\times (-3010)-\log [5,730 years]](https://tex.z-dn.net/?f=%5Clog%20%5BA%5D%3D%2014%20years%5Ctimes%20%28-3010%29-%5Clog%20%5B5%2C730%20years%5D)
![[A]=1.065\times 10^{-8}](https://tex.z-dn.net/?f=%5BA%5D%3D1.065%5Ctimes%2010%5E%7B-8%7D%20)
b)When , t = 
![\log [A]=t\log[\frac{1}{2}]-\log [t_{\frac{1}{2}}]](https://tex.z-dn.net/?f=%5Clog%20%5BA%5D%3Dt%5Clog%5B%5Cfrac%7B1%7D%7B2%7D%5D-%5Clog%20%5Bt_%7B%5Cfrac%7B1%7D%7B2%7D%7D%5D)
![\log [A]= 1.900\times 10^4 years\times (-3010)-\log [5,730 years]](https://tex.z-dn.net/?f=%5Clog%20%5BA%5D%3D%201.900%5Ctimes%2010%5E4%20years%5Ctimes%20%28-3010%29-%5Clog%20%5B5%2C730%20years%5D)
![[A]=0.000\times 10^{-3} [/tex](https://tex.z-dn.net/?f=%5BA%5D%3D0.000%5Ctimes%2010%5E%7B-3%7D%20%5B%2Ftex%20)
c)When , t = 
![\log [A]=t\log[\frac{1}{2}]-\log [t_{\frac{1}{2}}]](https://tex.z-dn.net/?f=%5Clog%20%5BA%5D%3Dt%5Clog%5B%5Cfrac%7B1%7D%7B2%7D%5D-%5Clog%20%5Bt_%7B%5Cfrac%7B1%7D%7B2%7D%7D%5D)
![\log [A]= 1.0000\times 10^5 years\times (-3010)-\log [5,730 years]](https://tex.z-dn.net/?f=%5Clog%20%5BA%5D%3D%201.0000%5Ctimes%2010%5E5%20years%5Ctimes%20%28-3010%29-%5Clog%20%5B5%2C730%20years%5D)
![[A]=0.0000\times 10^{-4}](https://tex.z-dn.net/?f=%5BA%5D%3D0.0000%5Ctimes%2010%5E%7B-4%7D%20)
Light is one form of energy that travels in electromagnetic waves. This energy is both magnetic and electrical. There are many different types of electromagnetic (EM) waves.
The answer is 3. The releasing of energy means exothermic reaction. So the ΔH should be negative. And the greatest quantity of energy released means that the greatest number. So according to the table I, the answer is 3.
<span>You would use the equation: Molarity M equals amount of solution over volume of solution. So, 0.758 M equals x L divided by 1.55 L OR 0.758 M = x L / 1.55 L . To solve: 1.55 multiplied by 0.758 equals 1.1479. The answer is 1.1479.</span>