+0  
 
0
119
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
 #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+88871 
+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

6 Online Users

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.