+0  
 
0
45
2
avatar

If 250 mg of a radioactive element decays to 200 mg in 12 hours, find the half-life of the element. (Round your answer to the nearest whole number.)

Guest Apr 19, 2018
Sort: 

2+0 Answers

 #1
avatar
+1

200 = 250 x 1/2^(12/t), where t=half-life
0.8 = 1/2^(12/t)            Take the natural log of both sides
-0.22314355 =(12/t) x -0.69314718      Cross multiply
-0.22314355 t =-8.317766                           Divide both sides by -0.22314355
t = 37.275 =~37 hours - the half-life of this material.

Guest Apr 19, 2018
 #2
avatar+86613 
+1

We have that

 

200 = 250(.5)^(12/h)   where h is the half-life in hours

Divide both sides by 250

200/250  = (.5)^(12/h)

.8  = (.5)^(t/h)      take the log of both sides

log (.8)  = log(.5)^(12/h)   

And by a log property we can write

log (.8) =  (12/h) log (.5)

 

Rearrange to isolate h

 

h  = 12log(.5) / log(.8)  ≈  37.28 hrs   

 

 

cool cool cool

CPhill  Apr 19, 2018

29 Online Users

avatar
New Privacy Policy (May 2018)
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  Privacy Policy